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Optical lens

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This additional condition is often the focal length of the lens, f, or the size of the object to image distance, in which case the sum of s1 + s2 is given by the size constraint of the system. In either case, all three variables are then fully determined.

Derivation oflens formula

If light is allowed to enter a darkened room through a tiny hole in a wall or door, the scenery outside will be projected onto the opposite wall. This phenomenon, known as pinhole projection, is one of the basic principles behind photography. The image created by pinhole projection is a reverse image, both upside-down, and left and right reversed. A pinhole camera can be easily created by opening a pinhole in a box that otherwise lets in no light. The hole should be covered with tape, and a sheet of photo printing paper placed inside, opposite the hole, without exposing it to light.

This puts a fundamental limitation on the geometry of an optics system. If an optical system of a given size is to produce a particular magnification, then there is only one lens position that will satisfy that requirement. On the other hand, a big advantage is that one does not need to make a direct measurement of the object and image sizes to know the magnification; it is determined by the geometry of the imaging system itself.

Lens formulaClass 10

Color film contains dye couplers, which, on development and fixation, become yellow, magenta or cyan, the three colors that are complementary to blue, green, and red. This is why a red apple appears green in a color negative. When light is shone through such a color negative onto color printing paper, the yellow, magenta and cyan colors in the negative create complementary colors in the paper, thus recreating the original colors of the subject photographed. This is the principle behind the dye coupler method of creating color images.

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Three rays are shown in Figure 1. Any two of these three rays fully determine the size and position of the image. One ray emanates from the object parallel to the optical axis of the lens. The lens refracts this beam through the optical axis at a distance f on the far side of the lens. A second ray passes through the optical axis at a distance f in front of the lens. This ray is then refracted into a path parallel to the optical axis on the far side of the lens. The third ray passes through the center of the lens. Since the surfaces of the lens are normal to the optical axis and the lens is very thin, the deflection of this ray is negligible as it passes through the lens.

The light that passes through a tiny hole in a wall creates an upside-down image of the scenery outside on the opposite wall of the room. Medieval European artists would capture such images on their canvases, tracing the details to make accurate sketches. The word "camera," in fact, derives from "camera obscura," the Latin term that the artists coined for such devices, which they used as an aid to creating their works. "Camera" means "room," while "obscura" means "ambiguous, dark." In short, cameras owe their name to a "dark room." It was in the first half of the 19th century that photography in the modern sense was born with the discovery of the technique of fitting a camera obscura with a metal plate that had been painted with a light-sensitive silver compound that automatically captured the pinhole image. In time, the metal plate became film, which then evolved from black-and-white to color film. In today's digital cameras, film has been replaced by light sensors that capture images by converting light into digital data.

Power oflens formula

This is valid in the paraxial approximation in which we have been working. Also, this development assumes perfect, aberration-free lenses. The addition of aberrations to our consideration would mean the replacement of the equal sign by a greater-than-or-equal sign in the statement of the invariant. That is, aberrations could increase the product but nothing can make it decrease.

How, then, does color film render color? Color film contains three layers of photo-sensitive emulsion that are sensitive to different wavelengths of light: red, green and blue, respectively. The layer that is sensitive to red light is normally applied first, followed by emulsions sensitive to green light, and then blue light as the topmost layer. Adding dyes to silver halides makes them sensitive only to specific wavelengths of light. When color film is exposed, each photosensitive layer absorbs light of a specific wavelength.

The Numerical Aperture (NA) is the most important number associated with the light gathering ability of an objective or condenser. It is directly related to ...

By ideal thin lens, we mean a lens whose thickness is sufficiently small that it does not contribute to its focal length. In this case, the change in the path of a beam going through the lens can be considered to be instantaneous at the center of the lens, as shown in the figure. In the applications described here, we will assume that we are working with ideally thin lenses. This should be sufficient for an introductory discussion. Consideration of aberrations and thick-lens effects will not be included here.

Lensequation

Now we are ready to look at what happens to an arbitrary ray that passes through the optical system. Figure 4 shows such a ray. In this figure, we have chosen the maximal ray, that is, the ray that makes the maximal angle with the optical axis as it leaves the object, passing through the lens at its maximum clear aperture. This choice makes it easier, of course, to visualize what is happening in the system, but this maximal ray is also the one that is of most importance in designing an application. While the figure is drawn in this fashion, the choice is completely arbitrary and the development shown here is true regardless of which ray is actually chosen.

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Focal length size guide ; 35mm - 85mm. Standard. Street, travel, portrait ; 85mm - 135mm. Short telephoto. Street photography and portraits ; 135mm+. Medium ...

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This is why chemical agents that reduce silver halides to silver are known as "developers." Even with development, those areas not affected by light remain as silver halides. They are removed by placing the film in a different agent that dissolves silver halides, leaving only the black silver grains. This is known as "fixing." A negative, which is an image in which the areas exposed to light appear as shades of black, is thus made by first taking a photo to create a latent image on the film, then developing and fixing that image with chemical agents. If printing paper is placed beneath the negative, and light is shone on the negative, the negative's blackened areas show up as lighter shades. Whiter areas show up as darker shades on the paper when that in turn is developed and fixed. This is the principle of black-and-white photography.

The quantity M is the magnification of the object by the lens. The magnification is the ratio of the image size to the object size, and it is also the ratio of the image distance to the object distance.

The box should then be pointed in the direction of the scenery to be filmed, and the tape removed from the pinhole to allow light in for a few seconds. If the printing paper is placed in developing solution, the scenery will gradually appear in reverse on the printing paper. Present-day cameras work on the same principle, but with a lens, aperture ring and shutter affixed to the pinhole to adjust focus and light, and film or CCD to replace the wall or printing paper.

Magnification oflens formula

The mechanism of faithfully rendering a picture made by light was first utilized by medieval European artists. However, a giant leap forward was achieved with the invention of film, and photography has continued to evolve into the present-day digital technology.

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Lens formulafor convexlens

This arbitrary ray goes through the lens at a distance x from the optical axis. If we again apply some basic geometry, we have, using our definition of the magnification

In recent years, digital cameras have become increasingly popular as an alternative to cameras that use film. A digital image is a long string of 1s and 0s representing all the colored light dots, known as pixels, which collectively make up the image. Digital cameras employ image sensors, such as CCDs or CMOS sensors, in place of film. CCDs are collections of tiny, light-sensitive diodes that convert light into electrical charges, which are then digitized to create a digital image. Digital cameras, too, work on the principle of filtering the three primary colors of red, green and blue. CMOS and CCD sensors resemble black-and-white film in that they respond only to the strength of light.

This is the Gaussian lens equation. This equation provides the fundamental relation between the focal length of the lens and the size of the optical system. A specification of the required magnification and the Gaussian lens equation form a system of two equations with three unknowns: f, s1, and s2. The addition of one final condition will fix these three variables in an application.

Camera film uses silver halides (such as silver chloride, bromide or iodide) as the materials exposed to light. When the silver halide layer absorbs light, electrons within the layer attach to the halide crystals, creating what are known as sensitivity specks. Light accordingly effects chemical changes in the silver-halide layer, leaving a latent image on the film. When exposed film is placed in a developing agent, the surroundings of the sensitivity specks are converted to silver, as a result of which the exposed areas start to turn black, and the image begins to "be developed."

We can use basic geometry to look at the magnification of a lens. In Figure 2, we have the same ray tracing figure with some particular line segments highlighted. The ray through the center of the lens and the optical axis intersect at an angle φ. Recall that the opposite angles of two intersecting lines are equal. Therefore, we have two similar triangles. Taking the ratios of the sides, we have

This is a fundamental law of optics. In any optical system comprising only lenses, the product of the image size and ray angle is a constant, or invariant, of the system. This is known as the optical invariant. The result is valid for any number of lenses, as could be verified by tracing the ray through a series of lenses. In some optics textbooks, this is also called the Lagrange Invariant or the Smith-Helmholz Invariant.

In digital cameras, the light beam is split light into its RGB elements before striking the light sensor, which then reads the strength of each color per pixel, and converts that information into digital data. Unlike film, digital images do not deteriorate with age, and can be enjoyed in various ways, such as viewing on a TV or PC screen, or by outputting them using a printer.

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In addition to the assumption of an ideally thin lens, we also work in the paraxial approximation. That is, angles are small and we can substitute θ in place of sin θ.

Let’s now go back to our ray tracing diagram and look at one more set of line segments. In Figure 3, we look at the optical axis and the ray through the front focus. Again looking at similar triangles sharing a common vertex and, now, angle η, we have