Chapter 23, Problem 66P

A double concave lens has surface radii of 33.4 cm and 28.8 cm. What is the focal length if n =1.52?

To determine

The focal length of a double concave lens

Answer to Problem 66P

Solution:

The focal length of the lens is -29.74 cm.

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:

$\begin{array}{l}{r}_1=-\text{33}.\text{4 cm}\\ r_2=\text{28}.\text{8 cm}\end{array}$

Using lensmaker’s formula,

$\frac{1}{f}=(1.52-1)\left(-\frac{1}{33.4}-\frac{1}{28.8}\right)$

This gives, $f=-\text{29}.\text{74 cm}$