Question

A thin lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. Applying the formula for image formation by a single spherical surface successively at the two surfaces of a lens, one can obtain the 'lens maker formula' and then the 'lens formula'. A lens has two foci - called 'first focal point' and 'second focal point' of the lens, one on each side.

Hint:

The lens maker formula gives the focal length of a lens based on the radii of curvature of its surfaces and its refractive index. The lens formula relates the focal length, object distance, and image distance.

Answer 1

A thin lens, defined as a transparent optical medium with two spherical surfaces, can be modeled as the combination of these two surfaces. The lens maker's formula determines the lens's focal length \( f \), incorporating the refractive index \( n \), the radii of curvature \( R_1 \) and \( R_2 \) of the two surfaces, and potentially the lens thickness. The formula is: \[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] Key variables are:
\( f \) denotes the focal length of the lens,
\( R_1 \) and \( R_2 \) represent the radii of curvature for the first and second spherical surfaces, respectively,
\( n \) is the refractive index of the lens material.

For a thin lens, the lens formula is expressed as: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where:
\( f \) is the focal length,
\( v \) is the image distance (from lens to image),
\( u \) is the object distance (from lens to object).
A lens possesses two focal points, one situated on each side.