Calculate focal lengthfrom image

\[\mathrm { BFL } = \dfrac { \mathrm { f } _ { 2 } \left( \mathrm { d } - \mathrm { f } _ { 1 } \right) } { \mathrm { d } - \left( \mathrm { f } _ { 1 } + \mathrm { f } _ { 2 } \right) }\]

A good sturdy tripod is a must. You’ll need a bit of weight so it holds your camera firmly and still for long periods of time.You will also need a cable release or remote trigger. This is so you can use your camera on a setting called bulb. I’ll teach you all about bulb in the next tutorial when I’m out and about. You can get these quite cheaply of the internet, just type in ‘cable release for …..your camera model.I also recommend you avoid variable ND filters. It’s harder to judge your exposure times with these types and on its strongest setting you can sometimes get lines going through the image. I would recommend getting a 10 stop and a 6 stop filter to get you started. You’ll have loads of fun with them.

And there you go, ND filters explained. Don’t forget to check out the ‘How to use ND filters tutorial’, where I’ll be out in the field using them. You can also download the free Guide to ND filters via the link above.

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\[\dfrac { 1 } { \mathrm { d } _ { o } } + \dfrac { 1 } { \mathrm { d } _ { \mathrm { i } } } = \dfrac { 1 } { \mathrm { f } }\]

And here is a shot taken just after that one using a 10 stop ND filter. The filter has allowed me to increase the exposure time to 30 seconds. I’ve still exposed the camera to same amount of light, but this one has been exposed over a longer period of time. When you do that everything that’s still, stays still, i.e. the tree and mountains and everything that moves blurs or blends together. This shot has also been adjusted in Lightroom to pump up the colours and contrast. Check out my other tutorial on how I adjust images in Lightroom if you wish. 30 Secs, f22, ISO 400

An ND filter acts like sunglasses would to your eyes, it blocks light coming into the lens like sunglasses blocks light coming into your eyes. ND stands for Neutral Density which means it blocks the light in a neutral way without changing the colour of the light.

Howtocalculate focal lengthof parabola

In this tutorial, I’m going to give you a guide to ND filters in photography; what ND filters do, what ND filters to buy, what effects they create and so on. I’ve also created an ND filters guide that you can download and keep. This will help you work out shutter speed times using our exposure calculator and advise on what ones to buy.If you’re thinking of buying or using ND filters to create long exposure effects, then this tutorial is for you.

Light is good, right? It’s what makes the image. It makes sense to think that if you block light coming into your lens you’re just going to make a dark, underexposed image.Well, when you block light coming into your lens you’re are forced to expose the camera to light for a longer period of time. You have to open the shutter for longer to allow for the correct amount of light to enter the camera.

The most common type of achromat is the achromatic doublet, which is composed of two individual lenses made from glasses with different amounts of dispersion Typically, one element is a negative (concave) element made out of flint, which has relatively high dispersion, and the other is a positive (convex) element made of crown glass, which has lower dispersion. The lens elements are mounted next to each other, often cemented together, and shaped so that the chromatic aberration of one is counterbalanced by that of the other.

If the separation distance is equal to the sum of the focal lengths (d = f1+f2), the combined focal length and BFL are infinite. This corresponds to a pair of lenses that transform a parallel (collimated) beam into another collimated beam (see ). This type of system is called an afocal system, since it produces no net convergence or divergence of the beam. Two lenses at this separation form the simplest type of optical telescope. Although the system does not alter the divergence of a collimated beam, it does alter the width of the beam. The magnification of such a telescope is given by

The signs of the lens’ radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but for our treatment if R1 is positive the first surface is convex, and if R1 is negative the surface is concave. The signs are reversed for the back surface of the lens: if R2 is positive the surface is concave, and if R2 is negative the surface is convex. If either radius is infinite, the corresponding surface is flat. With this convention the signs are determined by the shapes of the lens surfaces, and are independent of the direction in which light travels through the lens.

ND filters are created in stops. A stop in photography is either halving or doubling the amount of light e.g. making the picture 1 stop darker or 1 stop lighter. In the case of ND filters, you are always halving or reducing the amount of light. So a 1 stop ND filter will be stopping the light by 50% or half. A 10 stop filter is stopping the light by 10 halves in a row. You have to do it sequentially, that’s important.Remember when you’re doing long exposure shots it’s only the shutter speed you want to be changing. If you have a 2 second exposure without a filter, then you put a 1 stop ND filter on, you have effectively halved the amount of light coming into that camera. So to counter balance this you have to increase the amount of time you let light into the camera, in this case by doubling it. See table below.

Lenses are found in a huge array of optical instruments, ranging from the simple magnifying glass to a camera lens to the lens of the human eye. The word lens derives from the Latin word for lentil bean—the shape of which is similar to that of the convex lens (as shown in ). The convex lens is shaped so that all light rays that enter it parallel to its axis cross one another at a single point on the opposite side of the lens. The axis is defined as a line normal to the lens at its center (as shown in ). Such a lens is called a converging (or convex) lens for the corresponding effect it has on light rays. The expanded view of the path of one ray through the lens illustrates how the ray changes direction both as it enters and as it leaves the lens.

An achromatic lens or achromat is a lens that is designed to limit the effects of chromatic and spherical aberration. Achromatic lenses are corrected to bring two wavelengths (typically red and blue/violet) into focus in the same plane.

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Using paper, pencil, and a straight edge, ray tracing can accurately describe the operation of a lens. The rules for ray tracing for thin lenses are based on the illustrations included in this section:

Since the index of refraction of the lens is greater than that of air, the ray moves towards the perpendicular as it enters, and away from the perpendicular as it leaves (this is in accordance with the law of refraction). Due to the lens’s shape, light is thus bent toward the axis at both surfaces. The point at which the rays cross is defined as the focal point F of the lens. The distance from the center of the lens to its focal point is defined as the focal length f of the lens. shows how a converging lens, such as that in a magnifying glass, can concentrate (converge) the nearly parallel light rays from the sun towards a small spot.

Howtocalculate focal lengthPhysics

Achromatic Doublet: (a) Chromatic aberration is caused by the dependence of a lens’s index of refraction on color (wavelength). The lens is more powerful for violet (V) than for red (R), producing images with different locations and magnifications. (b) Multiple-lens systems, such as this achromatic doublet, can partially correct chromatic aberrations, but they may require lenses of different materials and add to the expense of optical systems such as cameras.

The filter holder typeCons - A lot more expensive. This system is for a commitment to this type of photography, or for those who have the money to spare – the other is for a practice or play around.Pros - Better quality. You can use them with other lenses but you will need an adapter ring for different lens. You can use ND filters in conjunction with other filters like the ND grad filters.

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double convex, or just convex) if both surfaces are convex. If the lens is biconvex, a beam of light travelling parallel to the lens axis and passing through the lens will be converged (or focused) to a spot on the axis, at a certain distance behind the lens (i.e. the focal length). In this case, the lens is called a positive or converging lens. See for a diagram of a positive (converging) lens.

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The focal length f is positive for converging lenses, and negative for diverging lenses. The reciprocal of the focal length, 1/f, is the optical of the lens. If the focal length is in meters, this gives the optical power in diopters (inverse meters).

What isfocal lengthof lens

The greater effect a lens has on light rays, the more powerful it is said to be. For example, a powerful converging lens will focus parallel light rays closer to itself and will have a smaller focal length than a weak lens. The light will also focus into a smaller, more intense spot for a more powerful lens. The power P of a lens is defined as the inverse of its focal length. In equation form:

If two thin lenses are separated in air by some distance d (where d is smaller than the focal length of the first lens), the focal length for the combined system is given by

ND Grads are mainly used to darken down skies and balance out your exposure.Below is an example using a hard grad ND filter. The one on the left is a normal picture shot using the camera’s built in light meter. This is what the camera thought was the correct exposure. The one on the right with the 2 stop hard grad ND filter. This has darkened the sky by 2 stops to give a much more balanced exposure.

Howtocalculate focal lengthfrom power

Focal lengthof lens formula

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\[\dfrac { \mathrm { h } _ { \mathrm { i } } } { \mathrm { h } _ { \mathrm { o } } } = - \dfrac { \mathrm { d } _ { \mathrm { i } } } { \mathrm { d } _ { \mathrm { o } } } = \mathrm { m }\]

For long exposure shots like below with clear water and blurred clouds you will want a 6 stop or 10 stop ND filter as this will give you an exposure time of at least 30 seconds and up to 4 minutes. The higher stop filters will enable you to get those long exposures.

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Consider an object some distance away from a converging lens, as shown in. To find the location and size of the image formed, we trace the paths of selected light rays originating from one point on the object (in this case the top of the person’s head). The figure shows three rays from the top of the object that can be traced using the five ray tracing rules. Rays leave this point going in many directions, but we concentrate on only a few with paths that are easy to trace. The first ray is one that enters the lens parallel to its axis and passes through the focal point on the other side (rule 1). The second ray passes through the center of the lens without changing direction (rule 3). The third ray passes through the nearer focal point on its way into the lens and leaves the lens parallel to its axis (rule 4). The three rays cross at the same point on the other side of the lens. The image of the top of the person’s head is located at this point. All rays that come from the same point on the top of the person’s head are refracted in such a way as to cross at the point shown. Rays from another point on the object, such as her belt buckle, will also cross at another common point, forming a complete image, as shown. Although three rays are traced in, only two are necessary to locate the image. It is best to trace rays for which there are simple ray tracing rules. Before applying ray tracing to other situations, let us consider the example shown in in more detail.

For rays passing through matter, the law of refraction is used to trace the paths. Here we use ray tracing to help us understand the action of lenses in situations ranging from forming images on film to magnifying small print to correcting nearsightedness. While ray tracing for complicated lenses, such as those found in sophisticated cameras, may require computer techniques, there is a set of simple rules for tracing rays through thin lenses. A thin lens is defined to be one whose thickness allows rays to refract, as illustrated in, but does not allow properties such as dispersion and aberrations. An ideal thin lens has two refracting surfaces but the lens is thin enough toassume that light rays bend only once. Another way of saying this is that the lens thickness is much much smaller than the focal length of the lens. A thin symmetrical lens has two focal points, one on either side and both at the same distance from the lens. (See. ) Another important characteristic of a thin lens is that light rays through its center are deflected by a negligible amount, as seen in the center rays in the first two figures. The treatment of a lens as a thin lens is known as the “thin lens approximation. ”

Calculate focal lengthfrom FOV

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If you want that glass looking effect in the water you need the water to be fairly still and calm, just slight ripples is perfect. Big crashing waves and rough seas will not work that well for this smooth glass effect. Also have a few clouds in the sky, this will give the shot texture. A fully overcast day will just give you a grey sky and although clear skies can look good a bit of texture up there adds to the shot. And try to catch the sunrise or sunset. Midday light will be too white and may even be too bright to get a 30 second or above exposure.

Then for shots like the one below you will want a 2 stop filter. This was shot at 1/15th of a second in the middle of the day. Because there was a lot a light I needed to stop the light down slightly so I could open my shutter for longer.

In contrast to a simple lens, which consists of only one optical element, a compound lens is an array of simple lenses (elements) with a common axis. The use of multiple elements allows for the correction of more optical aberrations, such as the chromatic aberration caused by the wavelength-dependent index of refraction in glass, than is possible using a single lens. In many cases these aberrations can be compensated for to a great extent by using a combination of simple lenses with complementary aberrations.

In subsequent sections we will examine the technique of ray tracing to describe the formation of images by lenses. Additionally, we will explore how image locations and characteristics can be quantified with the help of a set of geometric optics equations.

The simplest case is where lenses are placed in contact: if the lenses of focal lengths f1 and f2 are “thin”, the combined focal length f of the lenses is given by

In many cases both of these equations are referred to together as the thin lens equations. The thin lens equations are broadly applicable to all situations involving thin lenses (and “thin” mirrors).

If the lens is biconcave, a beam of light passing through the lens is diverged (spread); the lens is thus called a negative or diverging lens. The beam after passing through the lens appears to be emanating from a particular point on the axis in front of the lens; the distance from this point to the lens is also known as the focal length, although it is negative with respect to the focal length of a converging lens. See for a diagram of a negative (diverging) lens.

Ray Diagrams, Concave Lens and Convex Mirror: Shows how to draw the ray diagrams for locating the image produced by a concave lens and a convex mirror.

Let’s look at them both together. The one on the left, shot at 1/30th of a second, the one on the right, shot at 30 seconds with a 10 stop ND filter on. Again, they have both been exposed to exactly the same amount of light, but with the ND filter on you able to let that light in slowly which allows moving things to blur, such as the clouds, and it also allows things to blend in, such as the ripples in the water. Also note that it is only the shutter speed that has changed. The aperture and ISO stay the same when you are doing these shots and you must shoot in fully manual mode. I cover that in much more detail in my other tutorial ‘How to use ND filters’.

Keplerian Telescope: All refracting telescopes use the same principles. The combination of an objective lens 1 and some type of eyepiece 2 is used to gather more light than the human eye could collect on its own, focus it 5, and present the viewer with a brighter, clearer, and magnified virtual image 6. The magnification can be found by dividing the focal length of the objective lens by the focal length of the eyepiece.

Just to confuse you more, different manufacturers will advertise different numbers for stops. For instance, instead of saying a 2 stop ND filter, they might say it has an ‘optical density of 0.6’ or a ‘ND factor of 4’. To help you out with this here is another table giving you all these different numbers which mean the same thing.

How does a lens form an image of an object? We can use the technique of ray tracing to illustrate how lenses form images. We can also develop equations to describe the images quantitatively. Recall the five basic rules of ray tracing:

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Magnifying Glass: Sunlight focused by a converging magnifying glass can burn paper. Light rays from the sun are nearly parallel and cross at the focal point of the lens. The more powerful the lens, the closer to the lens the rays will cross.

shows the effect of a concave lens on rays of light entering it parallel to its axis (the path taken by ray 2 in the figure is the axis of the lens). The concave lens is a diverging lens, because it causes the light rays to bend away (diverge) from its axis. In this case, the lens is shaped so that all light rays entering it parallel to its axis appear to originate from the same point F, defined as the focal point of a diverging lens. The distance from the center of the lens to the focal point is again called the focal length f of the lens. Note that the focal length and power of a diverging lens are defined as negative. For example, if the distance to F in is 5.00 cm, then the focal length is f=–5.00 cm and the power of the lens is P=–20 D. The expanded view of the path of one ray through the lens illustrates how the shape of the lens (given the law of refraction) causes the ray to follow its particular path and be diverged.

The lensmaker’s formula is used to relate the radii of curvature, the thickness, the refractive index, and the focal length of a thick lens.

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Howtocalculate focal lengthof convex lens

Several important distances appear in. We define do as the object distance—the distance of an object from the center of a lens. Image distance diis defined as the distance of the image from the center of a lens. The height of the object and height of the image are given the symbols ho and hi, respectively. Images that appear upright relative to the object have heights that are positive and those that are inverted have negative heights. Using the rules of ray tracing and making a scale drawing with paper and pencil, like that in, we can accurately describe the location and size of an image. But the real benefit of ray tracing is in visualizing how images are formed in a variety of situations. To obtain numerical information, we use a pair of equations that can be derived from a geometric analysis of ray tracing for thin lenses. The thin lens equation is:

In the most common type (shown in ), the positive power of the crown lens element is not quite equaled by the negative power of the flint lens element. Together they form a weak positive lens that will bring two different wavelengths of light to a common focus. Negative doublets, in which the negative-power element predominates, are also made.

We define the ratio of image height to object height (hi/ho) as the magnification m. The magnification is related to do, di, ho, and hi by the following relation:

Let’s look at the effect an ND filter can have on an image. Below is a normal picture with no filter, taken using a tripod at 1/30th of a second. You can see the ripples in the water and the clouds look clear, everything has been frozen for that fraction of a second. Exposure details - 1/30th sec, f22, ISO 400

The above equation can be greatly simplified if the lens thickness d is very small compared to R1 and R2. In this case, the thin lens approximation can then be made and the lensmaker’s equation can be approximated as

\[\mathrm { P } = \dfrac { 1 } { \mathrm { f } } \approx ( \mathrm { n } - 1 ) \left[ \dfrac { 1 } { \mathrm { R } _ { 1 } } - \frac { 1 } { \mathrm { R } _ { 2 } } \right]\]

\[\mathrm { P } = \dfrac { 1 } { \mathrm { f } } = ( \mathrm { n } - 1 ) \left[ \dfrac { 1 } { \mathrm { R } _ { 1 } } - \dfrac { 1 } { \mathrm { R } _ { 2 } } + \dfrac { ( \mathrm { n } - 1 ) \mathrm { d } } { \mathrm { nR } _ { 1 } \mathrm { R } _ { 2 } } \right]\]

which is the ratio of the input beam width to the output beam width. Note the sign convention: a telescope with two convex lenses (f1 > 0, f2 > 0) produces a negative magnification, indicating an inverted image. A convex plus a concave lens (f1 > 0 >f2) produces a positive magnification and the image is upright.

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That’s the basic principle of ND filters, they stop light coming into your camera which forces you to compensate by letting in light over a longer period of time. The table below shows this with a 1 second exposure adding different strengths of ND filters. Notice how the new exposure times double sequentially. E.g when you add a 4 stop ND filter you have to double the original exposure 4 times.

Image Formation with a Thin Lens: Ray tracing is used to locate the image formed by a lens. Rays originating from the same point on the object are traced—the three chosen rays each follow one of the rules for ray tracing, so that their paths are easy to determine. The image is located at the point where the rays cross. In this case, a real image—one that can be projected on a screen—is formed.

Because the index of refraction of a lens is greater than air, a ray moves towards the perpendicular as it enters and away as it leaves.

Unlike idealized thin lenses, real lenses have a finite thickness between their two surfaces of curvature. An ideal thin lens with two surfaces of equal curvature would have zero optical power, meaning that it would neither converge nor diverge light. A lens whose thickness is not negligible is called a thick lens. In this case, we can not simply assume that a light ray is only refracted once while traveling through the lens. Instead the extent of the refraction must be dependent on the thickness of the lens.

Convex Lens: Rays of light entering a converging lens parallel to its axis converge at its focal point F. (Ray 2 lies on the axis of the lens. ) The distance from the center of the lens to the focal point is the lens’s focal length f. An expanded view of the path taken by ray 1 shows the perpendiculars and the angles of incidence and refraction at both surfaces.

Diverging Lens: Rays of light entering a diverging lens parallel to its axis are diverged, and all appear to originate at its focal point F. The dashed lines are not rays—they indicate the directions from which the rays appear to come. The focal length f of a diverging lens is negative. An expanded view of the path taken by ray 1 shows the perpendiculars and the angles of incidence and refraction at both surfaces.

Thin Lens Equations for a Convex Lens: Shows how to use the thin lens equation to calculate the image distance, image height and image orientation for convex lenses when the object distance is greater the the focal length (f).

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Screw on TypeOnes that screw onto the front of your lens, ones that need to use a filter holder system and graduated ND filters, with the graduated ND filters it’s best to use a filter holder system.

Ray tracing is the technique of determining or following (tracing) the paths that light rays take. Experiments, as well as our own experiences, show that when light interacts with objects several times as large as its wavelength, it travels in straight lines and acts like a ray. (A ray is simply a straight line that originates at a point. ) Its wave characteristics are not pronounced in such situations. Since the wavelength of light is less than a micron (a thousandth of a millimeter), it acts like a ray in the many common situations in which it encounters objects larger than a micron, such as lenses.

Thick Converging Lens: Diagram of a positive (converging) lens. The lensmaker’s formula relates the radii of curvature, the index of refraction of the lens, the thickness of the lens, and the focal length.

The screw in types are very good value for money (around £10 or $15 each), you can get lots of different brands of these and they all do pretty much the same thing. If you’re just starting out I recommend getting one of these types that will fit your widest-angle lens or your standard zoom lens, this will be great for getting those long exposure landscape shots.

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There are lots of different ND filters brands and kits out there. We want to recommend to you what we think are the best whether you are on a budget or not. We have only recommended companies that we or our colleagues use.

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Then, using the filter holder system, you can add a 10 stop ND filter together with the ND hard grad, add some Lightroom and Photoshop trickery to it and you can get a shot like this.

Thin Lens: Thin lenses have the same focal length on either side. (a) Parallel light rays entering a converging lens from the right cross at its focal point on the left. (b) Parallel light rays entering a diverging lens from the right seem to come from the focal point on the right.

Lenses have the same focal length when light travels from the back to the front as when light goes from the front to the back, although other properties of the lens, such as the aberrations are not necessarily the same in both directions.

There are many brands and they are all pretty good. Here are some brand names - HiTech, Lee, Nisi and cokin, the latter being the more budget brand.

Negative Diverging Lens: Diagram of a negative (diverging) lens. The lensmaker’s formula relates the radii of curvature, the index of refraction of the lens, the thickness of the lens, and the focal length.