Answer to Question #100645 in Optics for Cole Oluwaremilekun

Question

A convex lens those two faces has the same radius of curvature has a focal length of 16cm, refractive index of the glass is 1.2. find the radius curvature

Answer 1

Optics

We need to find the Radius of the curvature.

Solution:

Given, focal length = $f = 16 \space cm$

Refractive index of the glass $= n = 1.2$

Let R be the radius of curvature of each face.

then, $R_1 = R\\ R_2 = - R$

We know the Lens marker's formula

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

Plug the values in this formula

$$\frac {1}{16} =(1.2-1) [ \frac {1}{R} - \frac {1}{-R}]$$

$$\frac {1}{16} =(0.2) [ \frac {1}{R} + \frac {1}{R}]$$

$$\frac {1}{16} =(0.2) [ \frac {2}{R} ]$$

$$R = 0.2 \times 2 \times 16 \space cm$$

$$R = 6.4 \space cm$$

Answer: Yes

Radius of the curvature = R = 6.4 cm