Question

A drop of water is placed on a glass plate. $A$ double convex lens having radius of curvature of each surface $20\, cm$ is placed on it. The focal length of water lens $ \left( \mu =\frac{4}{3} \right),$ will be

• A. 0.20 m
• B. -0.60 m
• C. 0.30 m
• D. 0.40 m

Answer 1

Answer: (B)

From lens formula
$\frac{1}{f}=(\mu-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
where $R_{1}, R_{2}$ are radii of curvatures and $\mu$ the refractive index.
Given,
$R_{1} =-20 cm,$
$R_{2} =\infty$ (plano-convex lens),
$\mu =\frac{4}{3}$
$\frac{1}{f} =\left(\frac{4}{3}-1\right)\left(\frac{1}{-20}-\frac{1}{\infty}\right)$
$\Rightarrow \frac{1}{f}=\frac{1}{3} \times\left(-\frac{1}{20}\right)$
$\Rightarrow f=-60\, cm =-0.6\, m$