The focal length of a thin lens made from the material of refractive index 1.5 is 15 cm . When it is placed in a liquid of refractive index \(\frac{4}{3}\), its focal length will be ________ cm.

(D) 60
in air,
\(\frac{1}{f_{a}}=\left(\frac{n_{g}-n_{a}}{n_{a}}\right)\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right) \qquad\ldots(1)\)
in liquid,
\(\frac{1}{f_{w}}=\left(\frac{n_{g}-n_{w}}{n_{w}}\right)\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right) \qquad\ldots(2)\)
from equation (1) and (2),
\(\begin{aligned}
\frac{f_{w}}{f_{a}} & =\left(\frac{n_{g}-n_{a}}{n_{a}}\right) \times\left(\frac{n_{w}}{n_{g}-n_{w}}\right) \\
\frac{f_{w}}{15} & =\left(\frac{1.5-1}{1}\right) \times\left(\frac{\frac{4}{3}}{1.5-\frac{4}{3}}\right) \\
\frac{f_{w}}{15} & =4 \\
\therefore f_{w} & =60 \mathrm{~cm} \end{aligned}\)