BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

The focal point of a concave lens is the point where light rays parallel to the axis seem to diverge from after passing through the lens. The distance from the lens to this point is called the focal length of the lens. Because it seems rather odd to represent light as a dark line on a white page, the diagram above has been inverted below to show white light on a black background. The principle is the same. Now the question is where one would find parallel light rays in nature? How common or uncommon are parallel light rays if most of the light we seen on a daily basis is diverging to one degree or another? If an object is very far away, the angle formed between adjacent light rays is very small. Depending on the focal length of the specific lens, this distance might be anywhere from a few meters to a kilometer. If the object is very far, say 93,000,000 miles (1.5 x 1011 m) like the Sun, the distance is sufficiently far that light rays are essentially parallel. So sunlight is a convenient source of parallel light rays. Objects that are a great distance away like hills or trees also furnish rays that are almost parallel. Finally, lasers are a relatively inexpensive source of parallel light due to their inherent nature. NOTE: The light rays do not actually originate from the focal point. Rather, their behavior on the other side of the lens is such that they appear to be coming from there. Remember that the original light rays were parallel to the axis! NOTE 2: In the diagrams above, light rays are shown bending at the center of the lens. This is a construction technique and is used only for convenience. In fact the rays would bend once upon entering the lens and a second time upon exiting. BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Light spectrum

NOTE 2: In the diagrams above, light rays are shown bending at the center of the lens. This is a construction technique and is used only for convenience. In fact the rays would bend once upon entering the lens and a second time upon exiting. BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Speedof light

BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Each individual wavelength within the spectrum of visible light wavelengths is representative of a particular color. That is, when light of that particular wavelength strikes the retina of our eye, we perceive that specific color sensation. Isaac Newton showed that light shining through a prism will be separated into its different wavelengths and will thus show the various colors that visible light is comprised of. The separation of visible light into its different colors is known as dispersion. Each color is characteristic of a distinct wavelength; and different wavelengths of light waves will bend varying amounts upon passage through a prism. For these reasons, visible light is dispersed upon passage through a prism. Dispersion of visible light produces the colors red (R), orange (O), yellow (Y), green (G), blue (B), and violet (V). It is because of this that visible light is sometimes referred to as ROY G. BIV. (Incidentally, the indigo is not actually observed in the spectrum but is traditionally added to the list so that there is a vowel in Roy's last name.) The red wavelengths of light are the longer wavelengths and the violet wavelengths of light are the shorter wavelengths. Between red and violet, there is a continuous range or spectrum of wavelengths. The visible light spectrum is shown in the diagram below.

Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Visiblelight spectrum

When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Visiblelightwavelength

c. All regions have the same speed. The speed of a wave is not dependent upon its frequency and wavelength but rather upon the properties of the medium through which it travels.

NOTE: The light rays do not actually originate from the focal point. Rather, their behavior on the other side of the lens is such that they appear to be coming from there. Remember that the original light rays were parallel to the axis! NOTE 2: In the diagrams above, light rays are shown bending at the center of the lens. This is a construction technique and is used only for convenience. In fact the rays would bend once upon entering the lens and a second time upon exiting. BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Electromagneticspectrum

Now the question is where one would find parallel light rays in nature? How common or uncommon are parallel light rays if most of the light we seen on a daily basis is diverging to one degree or another? If an object is very far away, the angle formed between adjacent light rays is very small. Depending on the focal length of the specific lens, this distance might be anywhere from a few meters to a kilometer. If the object is very far, say 93,000,000 miles (1.5 x 1011 m) like the Sun, the distance is sufficiently far that light rays are essentially parallel. So sunlight is a convenient source of parallel light rays. Objects that are a great distance away like hills or trees also furnish rays that are almost parallel. Finally, lasers are a relatively inexpensive source of parallel light due to their inherent nature. NOTE: The light rays do not actually originate from the focal point. Rather, their behavior on the other side of the lens is such that they appear to be coming from there. Remember that the original light rays were parallel to the axis! NOTE 2: In the diagrams above, light rays are shown bending at the center of the lens. This is a construction technique and is used only for convenience. In fact the rays would bend once upon entering the lens and a second time upon exiting. BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

When we look at the cross-section of a concave lens we notice that the edges resemble prisms. In fact, a stack of prisms of varying angles can be used to simulate the actions of a concave lens. One such is shown here and is called a Fresnel Lens. Light passing through the angled prisms near the edges is bent significantly while light passing through the flat, central area is hardly bent at all. Light rays which are parallel to one another when approaching such an arrangement are spread out becoming diverging as shown here: We start with this general pattern to define the focal point for our concave lens.   DEFINITION 1: The focal point of a concave lens is the point where light rays parallel to the axis seem to diverge from after passing through the lens. The distance from the lens to this point is called the focal length of the lens. Because it seems rather odd to represent light as a dark line on a white page, the diagram above has been inverted below to show white light on a black background. The principle is the same. Now the question is where one would find parallel light rays in nature? How common or uncommon are parallel light rays if most of the light we seen on a daily basis is diverging to one degree or another? If an object is very far away, the angle formed between adjacent light rays is very small. Depending on the focal length of the specific lens, this distance might be anywhere from a few meters to a kilometer. If the object is very far, say 93,000,000 miles (1.5 x 1011 m) like the Sun, the distance is sufficiently far that light rays are essentially parallel. So sunlight is a convenient source of parallel light rays. Objects that are a great distance away like hills or trees also furnish rays that are almost parallel. Finally, lasers are a relatively inexpensive source of parallel light due to their inherent nature. NOTE: The light rays do not actually originate from the focal point. Rather, their behavior on the other side of the lens is such that they appear to be coming from there. Remember that the original light rays were parallel to the axis! NOTE 2: In the diagrams above, light rays are shown bending at the center of the lens. This is a construction technique and is used only for convenience. In fact the rays would bend once upon entering the lens and a second time upon exiting. BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Colorspectrum

The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Electromagnetic waves are able to travel through a vacuum - a region void of matter. Mechanical waves require a medium in order to propagate from one location to another.

DEFINITION 1: The focal point of a concave lens is the point where light rays parallel to the axis seem to diverge from after passing through the lens. The distance from the lens to this point is called the focal length of the lens. Because it seems rather odd to represent light as a dark line on a white page, the diagram above has been inverted below to show white light on a black background. The principle is the same. Now the question is where one would find parallel light rays in nature? How common or uncommon are parallel light rays if most of the light we seen on a daily basis is diverging to one degree or another? If an object is very far away, the angle formed between adjacent light rays is very small. Depending on the focal length of the specific lens, this distance might be anywhere from a few meters to a kilometer. If the object is very far, say 93,000,000 miles (1.5 x 1011 m) like the Sun, the distance is sufficiently far that light rays are essentially parallel. So sunlight is a convenient source of parallel light rays. Objects that are a great distance away like hills or trees also furnish rays that are almost parallel. Finally, lasers are a relatively inexpensive source of parallel light due to their inherent nature. NOTE: The light rays do not actually originate from the focal point. Rather, their behavior on the other side of the lens is such that they appear to be coming from there. Remember that the original light rays were parallel to the axis! NOTE 2: In the diagrams above, light rays are shown bending at the center of the lens. This is a construction technique and is used only for convenience. In fact the rays would bend once upon entering the lens and a second time upon exiting. BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Visiblelightfrequency

A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

1. A light wave is an electromagnetic wave that has both an electric and magnetic component associated with it. Electromagnetic waves are often distinguished from mechanical waves. The distinction is based on the fact that electromagnetic waves ______.

DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

As discussed in Unit 10 of The Physics Classroom Tutorial, electromagnetic waves are waves that are capable of traveling through a vacuum. Unlike mechanical waves that require a medium in order to transport their energy, electromagnetic waves are capable of transporting energy through the vacuum of outer space. Electromagnetic waves are produced by a vibrating electric charge and as such, they consist of both an electric and a magnetic component. The precise nature of such electromagnetic waves is not discussed in The Physics Classroom Tutorial. Nonetheless, there are a variety of statements that can be made about such waves.

Electromagneticspectrumwavelength

Electromagnetic waves exist with an enormous range of frequencies. This continuous range of frequencies is known as the electromagnetic spectrum. The entire range of the spectrum is often broken into specific regions. The subdividing of the entire spectrum into smaller spectra is done mostly on the basis of how each region of electromagnetic waves interacts with matter. The diagram below depicts the electromagnetic spectrum and its various regions. The longer wavelength, lower frequency regions are located on the far left of the spectrum and the shorter wavelength, higher frequency regions are on the far right. Two very narrow regions within the spectrum are the visible light region and the X-ray region. You are undoubtedly familiar with some of the other regions of the electromagnetic spectrum.

The focus of Lesson 2 will be upon the visible light region - the very narrow band of wavelengths located to the right of the infrared region and to the left of the ultraviolet region. Though electromagnetic waves exist in a vast range of wavelengths, our eyes are sensitive to only a very narrow band. Since this narrow band of wavelengths is the means by which humans see, we refer to it as the visible light spectrum. Normally when we use the term "light," we are referring to a type of electromagnetic wave that stimulates the retina of our eyes. In this sense, we are referring to visible light, a small spectrum from the enormous range of frequencies of electromagnetic radiation. This visible light region consists of a spectrum of wavelengths that range from approximately 700 nanometers (abbreviated nm) to approximately 400 nm. Expressed in more familiar units, the range of wavelengths extends from 7 x 10-7 meter to 4 x 10-7 meter. This narrow band of visible light is affectionately known as ROYGBIV.

Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

When all the wavelengths of the visible light spectrum strike your eye at the same time, white is perceived. The sensation of white is not the result of a single color of light. Rather, the sensation of white is the result of a mixture of two or more colors of light. Thus, visible light - the mix of ROYGBIV - is sometimes referred to as white light. Technically speaking, white is not a color at all - at least not in the sense that there is a light wave with a wavelength that is characteristic of white. Rather, white is the combination of all the colors of the visible light spectrum. If all the wavelengths of the visible light spectrum give the appearance of white, then none of the wavelengths would lead to the appearance of black. Once more, black is not actually a color. Technically speaking, black is merely the absence of the wavelengths of the visible light spectrum. So when you are in a room with no lights and everything around you appears black, it means that there are no wavelengths of visible light striking your eye as you sight at the surroundings.

BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Because it seems rather odd to represent light as a dark line on a white page, the diagram above has been inverted below to show white light on a black background. The principle is the same. Now the question is where one would find parallel light rays in nature? How common or uncommon are parallel light rays if most of the light we seen on a daily basis is diverging to one degree or another? If an object is very far away, the angle formed between adjacent light rays is very small. Depending on the focal length of the specific lens, this distance might be anywhere from a few meters to a kilometer. If the object is very far, say 93,000,000 miles (1.5 x 1011 m) like the Sun, the distance is sufficiently far that light rays are essentially parallel. So sunlight is a convenient source of parallel light rays. Objects that are a great distance away like hills or trees also furnish rays that are almost parallel. Finally, lasers are a relatively inexpensive source of parallel light due to their inherent nature. NOTE: The light rays do not actually originate from the focal point. Rather, their behavior on the other side of the lens is such that they appear to be coming from there. Remember that the original light rays were parallel to the axis! NOTE 2: In the diagrams above, light rays are shown bending at the center of the lens. This is a construction technique and is used only for convenience. In fact the rays would bend once upon entering the lens and a second time upon exiting. BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

If an object is very far away, the angle formed between adjacent light rays is very small. Depending on the focal length of the specific lens, this distance might be anywhere from a few meters to a kilometer. If the object is very far, say 93,000,000 miles (1.5 x 1011 m) like the Sun, the distance is sufficiently far that light rays are essentially parallel. So sunlight is a convenient source of parallel light rays. Objects that are a great distance away like hills or trees also furnish rays that are almost parallel. Finally, lasers are a relatively inexpensive source of parallel light due to their inherent nature. NOTE: The light rays do not actually originate from the focal point. Rather, their behavior on the other side of the lens is such that they appear to be coming from there. Remember that the original light rays were parallel to the axis! NOTE 2: In the diagrams above, light rays are shown bending at the center of the lens. This is a construction technique and is used only for convenience. In fact the rays would bend once upon entering the lens and a second time upon exiting. BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

We start with this general pattern to define the focal point for our concave lens.   DEFINITION 1: The focal point of a concave lens is the point where light rays parallel to the axis seem to diverge from after passing through the lens. The distance from the lens to this point is called the focal length of the lens. Because it seems rather odd to represent light as a dark line on a white page, the diagram above has been inverted below to show white light on a black background. The principle is the same. Now the question is where one would find parallel light rays in nature? How common or uncommon are parallel light rays if most of the light we seen on a daily basis is diverging to one degree or another? If an object is very far away, the angle formed between adjacent light rays is very small. Depending on the focal length of the specific lens, this distance might be anywhere from a few meters to a kilometer. If the object is very far, say 93,000,000 miles (1.5 x 1011 m) like the Sun, the distance is sufficiently far that light rays are essentially parallel. So sunlight is a convenient source of parallel light rays. Objects that are a great distance away like hills or trees also furnish rays that are almost parallel. Finally, lasers are a relatively inexpensive source of parallel light due to their inherent nature. NOTE: The light rays do not actually originate from the focal point. Rather, their behavior on the other side of the lens is such that they appear to be coming from there. Remember that the original light rays were parallel to the axis! NOTE 2: In the diagrams above, light rays are shown bending at the center of the lens. This is a construction technique and is used only for convenience. In fact the rays would bend once upon entering the lens and a second time upon exiting. BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

First, a concave lens is one which is thinner in the center than it is near the edges. This is shown in this diagram: When we look at the cross-section of a concave lens we notice that the edges resemble prisms. In fact, a stack of prisms of varying angles can be used to simulate the actions of a concave lens. One such is shown here and is called a Fresnel Lens. Light passing through the angled prisms near the edges is bent significantly while light passing through the flat, central area is hardly bent at all. Light rays which are parallel to one another when approaching such an arrangement are spread out becoming diverging as shown here: We start with this general pattern to define the focal point for our concave lens.   DEFINITION 1: The focal point of a concave lens is the point where light rays parallel to the axis seem to diverge from after passing through the lens. The distance from the lens to this point is called the focal length of the lens. Because it seems rather odd to represent light as a dark line on a white page, the diagram above has been inverted below to show white light on a black background. The principle is the same. Now the question is where one would find parallel light rays in nature? How common or uncommon are parallel light rays if most of the light we seen on a daily basis is diverging to one degree or another? If an object is very far away, the angle formed between adjacent light rays is very small. Depending on the focal length of the specific lens, this distance might be anywhere from a few meters to a kilometer. If the object is very far, say 93,000,000 miles (1.5 x 1011 m) like the Sun, the distance is sufficiently far that light rays are essentially parallel. So sunlight is a convenient source of parallel light rays. Objects that are a great distance away like hills or trees also furnish rays that are almost parallel. Finally, lasers are a relatively inexpensive source of parallel light due to their inherent nature. NOTE: The light rays do not actually originate from the focal point. Rather, their behavior on the other side of the lens is such that they appear to be coming from there. Remember that the original light rays were parallel to the axis! NOTE 2: In the diagrams above, light rays are shown bending at the center of the lens. This is a construction technique and is used only for convenience. In fact the rays would bend once upon entering the lens and a second time upon exiting. BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.

Light passing through the angled prisms near the edges is bent significantly while light passing through the flat, central area is hardly bent at all. Light rays which are parallel to one another when approaching such an arrangement are spread out becoming diverging as shown here: We start with this general pattern to define the focal point for our concave lens.   DEFINITION 1: The focal point of a concave lens is the point where light rays parallel to the axis seem to diverge from after passing through the lens. The distance from the lens to this point is called the focal length of the lens. Because it seems rather odd to represent light as a dark line on a white page, the diagram above has been inverted below to show white light on a black background. The principle is the same. Now the question is where one would find parallel light rays in nature? How common or uncommon are parallel light rays if most of the light we seen on a daily basis is diverging to one degree or another? If an object is very far away, the angle formed between adjacent light rays is very small. Depending on the focal length of the specific lens, this distance might be anywhere from a few meters to a kilometer. If the object is very far, say 93,000,000 miles (1.5 x 1011 m) like the Sun, the distance is sufficiently far that light rays are essentially parallel. So sunlight is a convenient source of parallel light rays. Objects that are a great distance away like hills or trees also furnish rays that are almost parallel. Finally, lasers are a relatively inexpensive source of parallel light due to their inherent nature. NOTE: The light rays do not actually originate from the focal point. Rather, their behavior on the other side of the lens is such that they appear to be coming from there. Remember that the original light rays were parallel to the axis! NOTE 2: In the diagrams above, light rays are shown bending at the center of the lens. This is a construction technique and is used only for convenience. In fact the rays would bend once upon entering the lens and a second time upon exiting. BOTTOM LINE: If we see a light ray that's parallel to the axis of a concave lens we know where it is going to go on the other side -- it will diverge as if it had started at the focal point.   DEFINITION 2: Converging light rays striking a concave lens but headed towards a point on the other side can be bent until they emerge parallel to the axis. The point that causes this to happen is called the focal point. Or as before, white light on a black background: NOTE: Because we have defined "focal point" so precisely, we can understand that a light ray that is not parallel to the axis will not diverge from the focal point on the other side of the lens. Also we know that a light ray that does not head towards the focal point will not emerge parallel to the axis.   BIG NOTE: A concave lens has two focal points - one on each side. They are equal distances from the lens. The lens does not have to have the same curvature on both sides for this to be true, and it doesn't depend on the direction the light takes entering the lens. It is the combined curvature that determines the focal point.   BIGGER NOTE: Because no light actually goes through the focal point of a concave lens, it isn't "real" like the focal point of a convex lens. Light is never focused there but only appears to come from the focal point. The focal point of a concave lens is called "virtual" which means that it only appears to have the effect of a focal point. When we purchase a concave lens, we specify the focal length with a negative number such as f = -5 cm. When the mathematics of image formation for concave lenses is worked out, it requires that we use a negative number for the focal length to get a correct answer.   HOW TO FIND THE FOCAL POINT: If you wish to find the focal point of a concave lens, you could take it outside on a clear day. Allow the sunlight to pass through the lens and observe the pattern formed on a screen that is parallel to the axis and located at the center of the lens. IMPORTANT: Make sure the sunlight is aimed along the axis of the lens. The pattern of light on the opposite side of the lens will be diverging. Trace at least two rays. You can place two pins in the path of the light and trace their shadows. Project these two paths back to where they intersect. This is the focal point. Remember, originally parallel rays diverge as if coming from the focal point.