Question

A thin glass (refractive index $1.5$) lens has optical power of $-5D$ in air. Its optical power in a liquid medium with refractive index $1.6$ will be:

• A. $25D$
• B. $-25D$
• C. $1D$
• D. None of these

Answer 1

Answer: (C)

$1D$

From lens makers formula,

Focal length in air, $\frac{1}{f_a}=(\frac{1.5}{1}-1)(\frac{1}{R_1}-\frac{1}{R_2})....\left(1\right)$

Focal length in liquid medium, $\frac{1}{f_m}=(\frac{{\mu }_g}{{\mu }_m}-1)(\frac{1}{R_1}-\frac{1}{R_2})$

$\frac{1}{f_m}=(\frac{1.5}{1.6}-1)(\frac{1}{R_1}-\frac{1}{R_2})....\left(ii\right)$

Dividing (i) by (ii), $\frac{f_m}{f_a}=\left(\frac{1.5-1}{\frac{1.5}{1.6}-1}\right)=-8$

$P_a=-5=\frac{1}{f_a}\Rightarrow f_a=-\frac{1}{5}$

$\Rightarrow f_m=-8\times f_a=-8\times -\frac{1}{5}=\frac{8}{5}$

$P_m=\frac{\mu }{f_m}=\frac{1.6}{8}\times 5=1D$