The relation between the object distance (p), the image distance (q), and the focal length (f) of a thin lens is given by the lens equation:

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Focal lengthformula

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Report the best value you have for the focal length of each lens, including the concave lens. Report any relationships that you have observed during the analysis, and comment on the difference between positive and negative lenses.

Gaussian Lens Equation ... y2/f = y1/(s1-f). ... y2/y1 = s2/s1 = f/(s1-f). ... 1/f = 1/s1 + 1/s2. This is the Gaussian lens equation. This equation provides the ...

Negative focal lengthdiverging lens

Repeat this procedure for each of the convex lenses at your station. Record the data for each lens in an organized manner for later analysis. Also, pick any two convex lens and carefully place them into a single lens holder. Repeat the procedures for measuring focal length for this lens combination. Finally, place the concave lens and the shortest focal length convex lens together in a lens holder, and measure the focal length of this combination.

When a beam of rays parallel to the principal axis of a lens impinges upon a converging lens, it is brought together at a point called the principal focus of the lens. The distance from the principal focus to the center of the lens is the focal length of the lens; the focal length is positive for a converging lens and negative for a diverging lens.

The hazard of driving, or performing other daily activities, with a large amount of glare in one's eyes has resulted in the development of polarized sunglasses. The lenses of such sunglasses contain polarizing filters that are oriented vertically with respect to the frames. Below, Figure 2 demonstrates how polarized sunglasses eliminate the glare from the surface of a highway. As illustrated, the electric field vectors of the blue light waves are oriented in the same direction as the polarizing lenses and, therefore, are passed through. In contrast, the red light wave represents glare, which is parallel to the surface of the highway. Since the red wave is perpendicular to the filters in the lenses, it is successfully blocked by the lenses.

The principal focal length of a converging lens may be determined by forming an image of a very distant object on a screen and measuring the distance from the lens to the screen. This distance will be the focal length, since rays of light from a very distant object are very nearly parallel. A more accurate method of determining the focal length of a positive lens is to measure the image distance corresponding to a suitable and known object distance, and to calculate the focal length from the lens equation (1).

A concave lens by itself cannot form a real image on a screen, since it is a diverging lens. Hence, a different method must be used for measuring its focal length. This is done by placing the negative lens in contact with a positive lens of shorter focal length whose focal length is known. The equivalent focal length of the combination can be measured experimentally, and the focal length of the negative lens computed using equation (3).

Focal lengthof concave lens is positive ornegative

where n is the refractive index of the medium, q(i) is the angle of incidence, and q(r) is the angle of refraction. When incident light is polarized in this way, it is often referred to as glare. On unusually bright days, the glare caused by sunlight on a roadway or a field of snow, may be almost blinding to the human eye.

Natural sunlight and most forms of artificial illumination transmit light waves whose electric field vectors vibrate equally in all planes perpendicular to the direction of propagation. When their electric field vectors are restricted to a single plane by filtration, however, then the light is polarized with respect to the direction of propagation.

The basic concept of polarization is illustrated above in Figure 1. In this example, the electric field vectors of the incident light are vibrating perpendicular to the direction of propagation in an equal distribution of all planes before encountering the first polarizer, a filter containing long-chain polymer molecules that are oriented in a single direction. Only the incident light that is vibrating parallel to the polarization direction is allowed to continue propagating unimpeded. Therefore, since Polarizer 1 is oriented vertically, it only permits the vertical waves in the incident beam to pass. However, the waves that pass through Polarizer 1 are subsequently blocked by Polarizer 2 because it is oriented horizontally and absorbs all of the waves that reach it due to their vertical orientation. The act of using two polarizers oriented at right angles with respect to each other is commonly termed crossed polarization and is fundamental to the practice of polarized light microscopy.

Another interesting use of light polarization is the liquid crystal display (LCD) utilized in applications such as wristwatches, computer screens, timers, and clocks. These devices are based upon the interaction of rod-like liquid crystalline molecules with an electric field and polarized light waves. The liquid crystalline phase exists in a ground state that is termed cholesteric, in which the molecules are oriented in layers and each successive layer is slightly twisted, forming a spiral pattern. When a polarized light wave interacts with the liquid crystalline phase, the wave is twisted by an angle of approximately 90 degrees with respect to the incident wave. This angle is a function of the helical pitch of the cholesteric liquid crystalline phase, which is dependent upon the chemical composition of the molecules. However, the helical pitch may be fine-tuned if small changes are made to the molecules.

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Can focal length be negativeparabola

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A prime example of the basic application of liquid crystals in display devices is the seven-segment LCD numerical display illustrated in Figure 3. Here, the liquid crystalline phase is sandwiched between two glass plates that have seven electrodes, which can be individually charged, attached to them. Although the electrodes appear black in this example, they are transparent to light in real devices. As demonstrated in Figure 3, light passing through Polarizer 1 is polarized in the vertical direction and, when no current is applied to the electrodes, the liquid crystalline phase induces a 90 degree twist of the light and it can pass through Polarizer 2, which is polarized horizontally. This light can then form one of the seven segments on the display.

Can focal length be negativein concave mirror

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Polarization of light is also very useful in many aspects of optical microscopy. Microscopes may be configured to use crossed polarizers, in which case the first polarizer, described as the polarizer, is placed below the sample in the light path and the second polarizer, known as the analyzer, is placed above the sample, between the objective and the eyepieces. If the microscope stage is left empty, the analyzer blocks the light polarized by the polarizer and no light is visible. However, when a birefringent, or doubly refracting, sample is placed on the stage between the crossed polarizers, the microscopist can visualize various aspects of the sample. This is because the birefringent sample rotates the light, allowing it to successfully pass through the analyzer.

Negative focal lengthreal or virtual

There are several lenses at your work station. Two of them are double concave lenses, and the rest of them are double convex. Take one of the convex lenses and measure its focal length by focusing a distant object or light source on the screen. Use an object four or more meters from the lens to do this accurately. Measure the distance from the lens to the screen where the image is sharply focused as the focal length of the lens. Record the distance in a data table. Do the same for each of the convex lenses at your station.

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Most optical instruments in common usage have one or more lenses in them. Whether it is a microscope, a telescope, or even a simple magnifying glass, the crucial element is a lens. The formation of images by lenses is one of the most important studies in the field of optics. In particular, in this experiment you will measure the focal length of both positive and negative lenses, and examine a combination of thin lenses.

where feq is the equivalent focal length of the lens combination, and f1 and f2 are the focal lengths of the two lenses that make the combination.

When isfocal length negativein mirror

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With the object and screen still fixed in the same positions, move the lens back and forth along the optical bench until another position is found where sharp image is formed on the screen. Record the object and image distances for this location, as well as the image size.

When isfocal length negativein lens

Using the lens equation (1), calculate the focal length of each lens or lens combination. Since you have found two focused positions for each lens, you should compute two values of focal length for each lens from the data. Average these two values. Compare, using percent difference, this average value with the value found by focusing a distant object. What do you notice about the object and image distances for the two positions of the same lens?

When current is applied to the electrodes, however, the liquid crystalline phase aligns with the current and loses the cholesteric spiral pattern. Therefore, light passing through a charged electrode is not twisted and is blocked by Polarizer 2. By coordinating the voltage on the seven positive and negative electrodes, the display is capable of rendering the numbers 0 through 9. In this example, the upper right and lower left electrodes are charged and, consequently, block light from passing through them, which results in the formation of the number "2".

When two thin lenses are in contact, the equivalent focal length of the combination may be measured experimentally by one of the above methods. It may also be calculated in terms of the individual focal lengths as:

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The magnification produced by a lens (the linear magnification) is defined as the ratio of the height of the image to the height of the object. This can be shown, by the use of geometry for similar triangles, to be equal to the ratio of the image distance to the object distance. Thus

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From the lens combination using the concave lens, calculate the focal length of the concave (negative) lens. The algebraic value from the computation comes out negative, which is why it is called a negative lens. Why could you not measure the focal length of this concave lens by itself?

Even unpolarized incident light, such as natural sunlight, is polarized to a certain degree when it is reflected from an insulating surface like water or a highway. In such cases, the electric field vectors of light parallel to the insulating surface are reflected to a greater degree than vectors with different orientations. However, the optical properties of the surface primarily determine how much of the reflected light is polarized. For instance, the properties of mirrors make them very poor polarizers, while many transparent materials are excellent polarizers if the angle of incident light is within certain limits. The particular angle inducing maximum polarization is known as the Brewster angle and is expressed by the equation:

When you have completed this experimental activity, you should be able to: (1) define focal length; (2) differentiate between positive and negative lenses; (3) measure focal length for a single thin lens and for combinations of thin lenses; and (4) distinguish between a real image and a virtual image.

Measure the size of the grid object, and compute the magnification as the ratio of image size to object size for each set of data that you have. Compare this to the ratio of image distance to object distance (equation 2), using percent difference, for each data set. Look carefully at the two magnifications for the two positions of the same lens. What is the relationship between these magnifications?

Now you will determine the focal length of each lens by a different method, using the lens equation (1). Take the convex lens with the shortest focal length, and place it in a lens holder on the optical bench. Place the light source and grid object at one end of the optical bench, and place the white cardboard screen at a distance of about 5 times the focal length of the lens from the object, with the lens between the object and screen. Leave the object and screen fixed, and move the lens along the bench until a sharp image of the grid object forms on the screen. Measure the distance between the object and the lens, and between the lens and the screen, and record these in a data table. Also, measure the size of the image on the screen.