Question

A thin glass (refractive index $1.5$) lens has optical power of $–5\text{D}$ in air. Its optical power in a liquid medium with refractive index $1.6$ will be

• A. $-1\text{D}$
• B. $25\text{D}$
• C. $-25\text{D}$
• D. $1\text{D}$

Answer 1

The correct option is D $1\text{D}$

Given
${\mu }_g=1.5$
${\mu }_m=1.6$
optical power$=-5\text{D}$
By the lens maker formula
$\frac{1}{f_a}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})=(1.5-1)(\frac{1}{R_1}-\frac{1}{R_2})$

and

$\frac{1}{f_m}=\left(\frac{{\mu }_g-{\mu }_m}{{\mu }_m}\right)(\frac{1}{R_1}-\frac{1}{R_2})$

$\frac{1}{f_m}=(\frac{1.5}{1.6}-1)(\frac{1}{R_1}-\frac{1}{R_2})$

$f_m=-8\times f_a$
$f_m=-8\times \frac{-1}{5}=1.6\text{m}(\because f_a=\frac{1}{P}=-\frac{1}{5}\text{m})$

$P_m=\frac{\mu }{f_m}=\frac{1.6}{1.6}=1\text{D}$

Hence, option $\left(A\right)$ is correct.