Question

A glass convex lens has a focal length of $20$ cm in air. What will be its focal length, when it is completely immersed in a liquid of refractive index $1.63$ ? ( Given ${}_a{\mu }_g=1.5$)

• A. $f_1=-127.4cm$
• B. $f_1=125.4cm$
• C. $f_1=-120.4cm$
• D. $f_1=18.75cm$

Answer 1

The correct option is D $f_1=18.75cm$

$\begin{array}{c}{f}_{\text{air}}=20m{\mu }_g=1.5\\ {\mu }_L=1.63\\ \text{Using Lens formula}\\ \frac{1}{f_{\text{air}}}=({\mu }_g-1)(\frac{1}{R_1}-\frac{1}{R_2})\end{array}$

$\begin{array}{c}\frac{1}{20}=\left(0.5\right)(\frac{1}{R_1}-\frac{1}{R_2})-\left(i\right)\\ \text{No lens immersed in liquid}\\ \frac{1}{f_{\text{liq}}}=[\frac{{}_a{\mu }_1}{{}_a{\mu }_g}-1][\frac{1}{R_1}-\frac{1}{R_2}]\end{array}$

$\frac{1}{f_{liq}}=(\frac{1.63}{1.5}-1)(\frac{1}{R_1}-\frac{1}{R_2})-\left(ii\right)$

$\text{Dividing i/(ii)}$

$\begin{array}{c}\frac{f_{liq}}{20}=\frac{0.5}{(1.63-1.55)}\times 1.5\\ f_{liq}=\frac{0.5\times 1.5\times 20}{0.8}\\ =18.75cm\end{array}$