Chapter 23, Problem 67P

To determine

The refractive index of the lens material when it has two convex surfaces of radii of curvature 34.1 cm and focal length 28.9 cm.

Answer to Problem 67P

Solution:

The refractive index is 1.59.

Explanation of Solution

Formula used:

Lens maker’s formula $\frac{1}{f}=(1.52-1)\left(-\frac{1}{22}+\frac{1}{18.5}\right)$ where f is the focal length, r₁ is the radius of curvature of first surfce and r₂ is radius of curvature (RoC)of second surface of the lens, positve when in the direction of optical path, otherwise negative. n is the refractive index of the lens material.

Calculation:

$\begin{array}{l}f=\text{28}.\text{9 cm}\\ r_1=-r_2=\text{ 34}.\text{1 cm}\end{array}$

Thus, using lens maker’s formula,

$\frac{1}{28.9}=(n-1)\frac{2}{34.1}$

This gives, n=1.59