A glass convex lens is of refractive index 1.55 with both faces of same radius of curvature. What is the…

A glass convex lens is of refractive index 1.55 with both faces of same radius of curvature. What is the radius of curvature required if focal length is to be $20 \mathrm{~cm}$ ?
  1. $21 \mathrm{~cm}$
  2. $18 \mathrm{~cm}$
  3. $20 \mathrm{~cm}$
  4. $22 \mathrm{~cm}$

Solution

Using the Lens maker's formula, $\begin{aligned} & f_1=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) \\ & \text { Here, } f=20 \mathrm{~cm}, \mu 1.55, R_1=R, R_2=-R \\ & \Rightarrow \frac{1}{20}=(1.55-1)\left(\frac{1}{R}-\frac{1}{(-R)}\right) \\ & \Rightarrow \frac{1}{20}=0.55 \times \frac{2}{R} \\ & \Rightarrow R=1.1 \times 20=22 \mathrm{~cm}\end{aligned}$ .

Asked in: MHT CET 2022 (06 Aug Shift 2)

Practice more Ray Optics questions on Aicharya