question_answer

A thin convex lens of focal length 10 cm and refractive index 1.5 is cut vertically into two equal pieces. They are placed as shown with a liquid of refractive index 3 between them. What is the focal length of the combination?

A)  -10 cm.               

B)  -10/4 cm.

C)  -10/3 cm.                           

D)  None

Correct Answer: C

Solution :

 \[\frac{1}{f}=(\mu -1)\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)\]            R = 10 cm. \[f'=(3-1)\left( \frac{1}{-10}-\frac{1}{10} \right)=-\frac{10}{4}\] \[\frac{1}{{{f}_{eq}}}=\frac{1}{20}-\frac{4}{10}+\frac{1}{20}=\frac{2}{20}-\frac{4}{10}\]\[\Rightarrow \]\[{{f}_{eq}}=-\frac{10}{3}cm\]