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 is a transparent optical medium with two spherical surfaces, and it can be treated as the combination of two spherical surfaces. The lens maker formula gives the focal length \( f \) of the lens in terms of the refractive index \( n \), the radii of curvature \( R_1 \) and \( R_2 \) of the two surfaces, and the thickness of the lens (if required). The formula is: \[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] where:
\( f \) is the focal length of the lens,
\( R_1 \) and \( R_2 \) are the radii of curvature of the first and second spherical surfaces of the lens, and
\( n \) is the refractive index of the material of the lens.

For a thin lens, the lens formula is given by: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where:
\( f \) is the focal length,
\( v \) is the image distance (distance from the lens to the image),
\( u \) is the object distance (distance from the lens to the object).
The lens has two foci, one on each side, known as the first focal point and the second focal point.