Question

A thin glass $(\mu =1.5)$ lens has power -5D in air. its power in a medium of refractive index 1.6 will be

• A. $\frac{5}{8}D$
• B. $\frac{25}{8}D$
• C. $-\frac{5}{8}D$
• D. $-\frac{25}{8}D$

Answer 1

Answer: (A)

$\frac{5}{8}D$

$f=\frac{1}{P}=\frac{1}{-5}=-0.2m$

$⟹f=-20cm$

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

$⟹\frac{-1}{20}=(1.5-1)(\frac{1}{R_1}-\frac{1}{R_2})$

$⟹(\frac{1}{R_1}-\frac{1}{R_2})=\frac{-1}{10}$

Now, in medium of refractive index ${\mu }_1=1.6$

$\frac{1}{f}=(\frac{\mu }{{\mu }_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$

$⟹\frac{1}{f}=(\frac{1.5}{1.6}-1)\times \frac{-1}{10}=\frac{0.1}{16}$

$⟹f=160cm=1.6m$

$P=\frac{1}{f}=\frac{1}{1.6}$

Hence, $P=\frac{5}{8}D$

Hence, answer is option-(A).