Question

A double convex lens of focal length $6$ cm is made of glass of refractive index $1.5$. The radius of curvature of one surface which is double that of the other surface will be

• A. $3cm$
• B. $9cm$
• C. $12cm$
• D. $24cm$

Answer 1

The correct option is B $9cm$

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

$\therefore f=\frac{R_1{R}_2}{(\mu -1)(R_1+R_2)}$

$=\frac{2R\times R}{(\mu -1)\times 3R}=\frac{2R}{3(\mu -1)}$

$\Rightarrow 6=\frac{2R}{2\left(0.5\right)}$

$\Rightarrow R=\frac{6\times 3\times \left(0.5\right)}{2}=4.5$

$\therefore R_1=2R$

$⟹R_1=9cm$