Question

13. A plano-convex lens of focal length 25.0 cm is to be made with crown glass of refractive index 1.52. Calculate the radius of curvature of the grinding and polishing tools to be used in making this lens.

Answer 1

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

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

We use the lens maker's formula

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

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 be:

$$\frac {1}{f} = (\mu-1) (\frac{1}{R_1})$$ $$\frac {1}{25} = (1.52 -1) (\frac {1}{R_1})$$ $$\frac {1}{25} =(0.52) (\frac {1}{R_1})$$ $$R_1 = 0.52 \times 25= 13 cm$$