Question

A double convex lens has power $P$ and same radii of curvature $R$ of both the surfaces. The radius of curvature of a surface of a plano - convex lens made of the same material with power $1.5P$ is :

• A. $2R$
• B. $\frac{R}{2}$
• C. $\frac{3R}{2}$
• D. $\frac{R}{3}$

Answer 1

The correct option is D $\frac{R}{3}$

Using lens maker's formula,

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

For double convex lens, $R_1=R_2=R$

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

$\Rightarrow P=\frac{1}{f}=(\mu -1)\frac{2}{R}...\left(i\right)$

For plano - convex lens,

$R_1=R^{\prime },R_2=\infty$

Using lens maker's formula again, we have

$1.5P=\frac{1}{f^{\prime }}=(\mu -1)(\frac{1}{R^{\prime }}-\frac{1}{\infty })$

$\Rightarrow \frac{3}{2}P=\frac{\mu -1}{R^{\prime }}...\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$,

$\frac{3}{2}=\frac{R}{2R^{\prime }}\Rightarrow R^{\prime }=\frac{R}{3}$

Hence, option $\left(\text{D}\right)$ is correct.