question_answer

. Shown in the figure here is a convergent lens placed inside a cell filled with a liquid. The lens has focal length + 20 cm when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is          [NSEP 1994; DPMT 2000]

A)            + 80 cm

B)            ? 80 cm

C)            ? 24 cm

D)            ?100 cm

Correct Answer: D

Solution :

                   \[\frac{1}{F}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}+\frac{1}{{{f}_{3}}}\]                                                                     \[\frac{1}{{{f}_{1}}}=(1.6-1)\left( \frac{1}{\infty }-\frac{1}{20} \right)=-\frac{0.6}{20}=-\frac{3}{100}\]   ?(i)                    \[\frac{1}{{{f}_{2}}}=(1.5-1)\left( \frac{1}{20}-\frac{1}{-20} \right)=\frac{1}{20}\]             ?(ii)                    \[\frac{1}{{{f}_{3}}}=(1.6-1)\left( \frac{1}{-20}-\frac{1}{\infty } \right)=-\frac{3}{100}\] ?(iii)            \[\Rightarrow \] \[\frac{1}{F}=-\frac{3}{100}+\frac{1}{20}-\frac{3}{100}\Rightarrow F=-100\]\[cm\]