Derive lens makers formula

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A lens is a transparent medium bounded by two curved surfaces usually spherical or cylindrical , although one of the surfaces of the lens may be a plane. The manufacturer of the lens selects the material of the lens and grinds its surface to make suitable radii of curvatures. He can therefore adjust the focal length of the lens. The lens maker's formula is a mathematical equation that relates the focal length of a thin lens to its refractive index and the radii of curvature of its two surfaces. It is given by the following equation:. The formula can be derived by considering the refraction of light through the lens.

Derive lens makers formula

However, not all lenses have the same shape. The vocabulary used to describe lenses is the same as that used for spherical mirrors: The axis of symmetry of a lens is called the optical axis, where this axis intersects the lens surface is called the vertex of the lens, and so forth. Likewise, a concave or diverging lens is shaped so that all rays that enter it parallel to its optical axis diverge, as shown in part b. To understand more precisely how a lens manipulates light, look closely at the top ray that goes through the converging lens in part a. Likewise, when the ray exits the lens, it is bent away from the perpendicular. The overall effect is that light rays are bent toward the optical axis for a converging lens and away from the optical axis for diverging lenses. For a converging lens, the point at which the rays cross is the focal point F of the lens. For a diverging lens, the point from which the rays appear to originate is the virtual focal point. The distance from the center of the lens to its focal point is the focal length f of the lens. In this case, the rays may be considered to bend once at the center of the lens. For the case drawn in the figure, light ray 1 is parallel to the optical axis, so the outgoing ray is bent once at the center of the lens and goes through the focal point. Another important characteristic of thin lenses is that light rays that pass through the center of the lens are undeviated, as shown by light ray 2. Ray tracing is the technique of determining or following tracing the paths taken by light rays. Ray tracing for thin lenses is very similar to the technique we used with spherical mirrors.

Sir, in mirror and lens derive lens makers formula derivations, we are using sign conventions, to generalise it, but then why are not doing the same here. For the case drawn in the figure, light ray 1 is parallel to the optical axis, so the outgoing ray is bent once at the center of the lens and goes through the focal point. Your result is as below.

Lenses of different focal lengths are used for various optical instruments. The derivation of lens maker formula is provided here so that aspirants can understand the concept more effectively. Lens manufacturers commonly use the lens maker formula for manufacturing lenses of the desired focal length. The complete derivation of the lens maker formula is described below. Using the formula for refraction at a single spherical surface, we can say that,. This is the lens maker formula derivation.

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Derive lens makers formula

A lens is a transparent medium bounded by two curved surfaces usually spherical or cylindrical , although one of the surfaces of the lens may be a plane. The manufacturer of the lens selects the material of the lens and grinds its surface to make suitable radii of curvatures. He can therefore adjust the focal length of the lens. The lens maker's formula is a mathematical equation that relates the focal length of a thin lens to its refractive index and the radii of curvature of its two surfaces. It is given by the following equation:. The formula can be derived by considering the refraction of light through the lens. But before moving directly to the derivation part, first, have a brief review regarding the sign convention adopted and assumptions to be made while doing derivation, which can be found in the later parts of this article only. Example 1. A biconvex lens has radii of 20 cm each. If the refraction Refractive index of the lens material is 1.

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Anurag Hooda. About About this video Transcript. Direct link to prisha. The image must be real, so you choose to use a converging lens. Watch Now. If ray tracing is required, use the ray-tracing rules listed near the beginning of this section. Let the refractive indices of the surrounding medium and the lens material be n 1 and n 2 , respectively. In this case, a real image—one that can be projected on a screen—is formed. However, for light that contains several wavelengths e. To understand more precisely how a lens manipulates light, look closely at the top ray that goes through the converging lens in part a. The negative magnification means that the image is inverted. As expected, the image is inverted, is real, and is larger than the object. For a diverging lens, a ray that approaches along the line that passes through the focal point on the opposite side exits the lens parallel to the axis ray 3 in part b.

Lenses of different focal lengths are used for various optical instruments. The derivation of lens maker formula is provided here so that aspirants can understand the concept more effectively.

Solution a. The angle of incidence and angle of refraction should be small. The problem is that, as we learned in the previous chapter, the index of refraction of a material depends on the wavelength of light. But why do we not take the object distance in the first refraction to be minus infinity Find the location, orientation, and magnification of the image for an 3. View Test Series. Lakshminaarayanan Vs. The focal length is positive, as expected for a converging lens. Thus, the image of the tip of the arrow is located at this point. Clearly, we know that in a biconvex lens, the centre of curvature of the first surface is on the positive side of the lens and that of the second surface is on the negative side. Solve these for the unknowns and insert the given quantities or use both together to find two unknowns. Oblique Parallel Rays and Focal Plane We have seen that rays parallel to the optical axis are directed to the focal point of a converging lens.