Answer to Question #101499 in Optics for Ekemini paul

Question

A plano convex lens of focal length 25cm is to be made with crown glass of refractive index 1.52. calculate the radius of the curvature of the grinding and polishing tools to be used in the lens

Answer 1

Optics

We need to calculate the radius of the curvature of the grinding and polishing tools.

Solution:

Given,

$f=$ Focal length of convex lens = $25 cm$

$\mu =$ refractive index of crown glass = $1.52$

We know the lens maker's formula

i.e.,

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

Here, $R_1 \space and \space R_2$ are the radii of the curvatures

For convex lens, $R_2 \space is \space flat$ , so $\frac {1}{R_2} =0$

So, the formula will becomes as below,

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

$$\frac {1}{25} = (1.52 -1) (\frac {1}{R_1})$$

$$\frac {1}{25} =(0.52) (\frac {1}{R_1})$$

$$R_1 = 0.52 \times 25= 13 cm$$

Answer: Yes