Derive lens makers formula

Lenses of different focal lengths are derive lens makers formula 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 nyse: tgt focal length. The complete derivation of the lens maker formula is described below.

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

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Search for courses, skills, and videos. Refraction in thin lenses. About About this video Transcript. Let's derive the famous lens makers formula. This formula only works for thin lenses. Created by Mahesh Shenoy. Want to join the conversation? Log in. Sort by: Top Voted.

Magnetic Flux Equation. To find the magnification and orientation of the image, derive lens makers formula, use. As shown in the figure, parallel rays focus where the ray through the center of the lens crosses the focal plane.

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.

We will discuss the form of the equation that is applicable only to thin lenses. This formula is only applicable to a lens of a given refractive index placed in air. We make the assumption that this is a thin lens as stated earlier , the points D , P and E in figure 1 have a very small distance between them, which can be neglected. Therefore, the radii of curvature of the left side of the lens is the distance C 2 E, approximately the same as the C 2 P — i. Consider the lens setup as shown in Figure 2. O is the point at which the object is placed on the principal axis of the lens. The above figure shows the image formation at I. Let the distance between the center of the lens P and the object O be u units, and the distance PI is v units.

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. Substitute a number in any field and the calculation will be initiated. Default values will be entered for any unspecified parameter, but the index and radius values may be changed. The second part of the calculation above shows the diminshed power of a lens in a medium other than air. This gives important insight into the role of the two lenses of the human eye. The cornea has the greatest power because light enters it from the air.

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Important Links. I think you should probably learn the textbook one. This is exactly the same equation as we obtained for mirrors see Equation 2. Image Formation by Thin Lenses We use ray tracing to investigate different types of images that can be created by a lens. Also, what is the magnification and orientation of the image? About About this video Transcript. The size of the image is given by. If you're seeing this message, it means we're having trouble loading external resources on our website. Sign in. In the case of a converging lens, these rays do not converge at the focal point.

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.

This is the lens maker formula derivation. Even if ray tracing is not used, a careful sketch is always very useful. Want to know more about this Super Coaching? This can be seen in the plot of part a of the figure, which shows that the image distance approaches asymptotically the focal length of 1 cm for larger object distances. Posted a month ago. Search for courses, skills, and videos. Is the lens maker formula the same for concave and convex lenses? In this case, a real image—one that can be projected on a screen—is formed. Posted a year ago. The distance from the center of the lens to its focal point is the focal length f of the lens. In other cases, the image is a virtual image, which cannot be projected onto a screen. A biconvex lens has radii of 20 cm each.