Question

The radii of curvature of the surfaces of a double convex lens are 20 cm and 40 cm respectively, and its focal length is 20 cm. What is the refractive index of the material of the lens?

• A. $\frac{5}{2}$
• B. $\frac{4}{3}$`
• C. $\frac{5}{3}$
• D. $\frac{4}{5}$

Answer 1

The correct option is C $\frac{5}{3}$

Given: The focal length of the double-convex lens is $20cm$.

The radius of curvature of the first convex surface is $20cm$.

The radius of curvature of the second convex surface is $40cm$.

To find: The refractive index of the lens material.

The relation between the focal length and the radius of curvature for the lens is given by:

$\frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2})$

For double-convex lens the radius of curvature are.

So, $R_1=+20,R_2=-40$

and $f=20$

Substitute the values.

$\frac{1}{20}=(n-1)(\frac{1}{20}+\frac{1}{40})$

$3n-3=2$

$n=\frac{5}{3}$