Question

A plano-convex lens is made of material of refractive index $1.6$. The radius of curvature of the curved surface is $60\text{cm}$. The focal length of the lens is

[Assume, surrounding medium to be air]

• A. $200\text{cm}$
• B. $100\text{cm}$
• C. $50\text{cm}$
• D. $400\text{cm}$

Answer 1

The correct option is B $100\text{cm}$


For a plano - convex lens ,

Radius of curvature of plane surface, $R_1=\infty$
Radius of curvature of curved convex surface, $R_2=-60\text{cm}$

From lens maker's formula,

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

$\Rightarrow$$\frac{1}{f}=(1.6-1)(\frac{1}{\infty }-\frac{1}{-60})$

$\Rightarrow$$\frac{1}{f}=0.6\times \frac{1}{60}$

$\therefore f=100\text{cm}$

Hence, option (b) is the correct answer.

Why this question? Note:- Focal length of a plano - convex lens is given by $$f=\frac{R}{{\mu }_{rel}-1}$$