Question

A liquid of refractive index $1.6$ is contained in the cavity of a glass specimen of refractive index $1.5$ as shown in figure. If each of the curved surfaces has a radius of curvature of $0.20\text{m}$, the arrangement behaves as a

• A. converging lens of focal length $0.25\text{m}$
• B. diverging lens of focal length $0.25\text{m}$
• C. diverging lens of focal length $0.17\text{m}$
• D. converging lens of focal length $0.72\text{m}$

Answer 1

The correct option is B diverging lens of focal length $0.25\text{m}$

According to the formula to find the focal length of the lens,
$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$
Power of liquid lens $=(1.6-1)\left(\frac{2}{0.20}\right)=\frac{6}{10}\times 10=6D$
Power of concave lens
$=(1.5-1)(-2/0.20)=-5D$
Total power of two concave lenses $=-10D$
Power of system $=-10D+6D=-4D$
Focal length $=\frac{1}{-4}=-0.25\text{m}$