Question

An equal-biconvex lens $(\mu =1.5)$ of focal length $20cm$ is cut into two parts and placed in contact as shown in the figure. A liquid of refractive index $1.3$ is filled between the two parts of lens. The equivalent focal length of the combination is

• A. $\frac{20}{3}cm$
• B. $50cm$
• C. $\frac{80}{3}cm$
• D. $30cm$

Answer 1

The correct option is B $50cm$

Hint: Consider three lenses are in contact
Sol: $R=20cm$
and therefore; $\frac{1}{f_2}=(1.3-1)\left(\frac{-2}{20}\right)=\frac{-3}{100}$
and therefore; $\frac{1}{f_e}=\frac{1}{20}-\frac{3}{100}\Rightarrow f_e=50cm$