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:.

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.

Sort by: Derive lens makers formula Voted. 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.

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. Put your understanding of this concept to test by answering a few MCQs.

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.

Derive lens makers formula

For a thin lens, the power is approximately the sum of the surface powers. The radii of curvature here are measured according to the Cartesian sign convention. For a double convex lens the radius R 1 is positive since it is measured from the front surface and extends right to the center of curvature. The radius R 2 is negative since it extends left from the second surface. The above calculation is a single purpose calculation which returns the powers and focal lengths based on the values of the radii and indices of refraction.

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The size of the image is given by. If ray tracing is required, use the ray-tracing rules listed near the beginning of this section. Likewise, when the ray exits the lens, it is bent away from the perpendicular. In the case of a converging lens, these rays do not converge at the focal point. Relation Between In Physics. Unfortunately, this phenomenon also leads to aberrations in images formed by lenses. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. 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 focal length of a thin lens is the same to the left and to the right of the lens. Go back to previous article.

We will discuss the form of the equation that is applicable only to thin lenses.

The focal length of a thin lens is the same to the left and to the right of the lens. The height of the object and the height of the image are indicated by h o and h i , respectively. About About this video Transcript. The image must be real, so you choose to use a converging lens. Show preview Show formatting options Post answer. Note that the image is in focus but the face is not, because the image is much closer to the camera taking this photograph than the face. Start Quiz. Make a list of what is given or can be inferred from the problem identify the knowns. Important Links. If you are checking this Physics article, also check the other Physics articles in the table below:.