Question

Write lens maker's formula for a thin lens. On its basis, discuss the effect of refractive index of lens material and radius of curvature of lens surfaces on its focal length.

Hint:

A higher refractive index and larger radii of curvature result in a longer focal length, whereas a smaller refractive index and smaller radii lead to a shorter focal length.

Answer 1

Step 1: Lens Maker's Formula.
The lens maker’s formula relates the focal length \( f \) of a thin lens to the refractive index of the lens material \( n \) and the radii of curvature of the two surfaces \( R_1 \) and \( R_2 \). The formula is given by: \[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] where: - \( n \) is the refractive index of the lens material, - \( R_1 \) is the radius of curvature of the first lens surface, - \( R_2 \) is the radius of curvature of the second lens surface.
Step 2: Effect of Refractive Index.
The focal length \( f \) is directly proportional to the refractive index \( n \). As the refractive index increases, the focal length of the lens decreases, making the lens more powerful (shorter focal length).
Step 3: Effect of Radius of Curvature.
The focal length \( f \) is also directly proportional to the radii of curvature \( R_1 \) and \( R_2 \). If the radii of curvature increase, the focal length increases, making the lens less powerful (longer focal length).