Chapter 23, Problem 70P

To determine

The radius of curvature of one surface of a lens

Answer to Problem 70P

Solution:

The RoC of the other surface is -34.3 cm

Explanation of Solution

Formula used:

Power in diopter is given by $=\frac{1000}{f(mm)}$

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:

$\begin{array}{l}{r}_1=\text{3}0\text{ cm}\\ f=\text{1}000/\text{3}.\text{5}=\text{285}.\text{71 mm}=\text{28}.\text{571 cm}\end{array}$

Using lens maker’s formula

$\frac{1}{28.571}=(1.56-1)\left(\frac{1}{30}-\frac{1}{r_2}\right)$

This gives, $r_2=-\text{34}.\text{3 cm}$