Question

Diameter of aperture of a plano-convex lens is $6\, cm$ and thickness at the centre is $3\, mm$. If the speed of light in the material of the lens is $2 \times 10^8 \,m \,s ^{-1}$, the focal length of the lens is

• A. $15\,cm$
• B. $20\,cm$
• C. $30\,cm$
• D. $10\,cm$

Answer 1

Answer: (C)

Here, $r=\frac{6}{2}=3\,cm$, $t=3\,mm=0.3\,cm$
If $ R_{2}$ is radius of curvature of convex surface , then $2R_{2}t =r^{2}$
$\therefore \, R_{2}=\frac{r^{2}}{2t}=\frac{3\times3}{2\times0.3}=15\,cm, R_{1}=\infty$
and $ \mu=\frac{c}{\upsilon}=\frac{3\times10^{8}}{2\times10^{8}}=\frac{3}{2}$
As $\frac{1}{f}=\left(\mu-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
$\therefore \frac{1}{f}=\left(\frac{3}{2}-1\right)\left(\frac{1}{\infty}-\frac{1}{15}\right)=\frac{1}{30}$
$\Rightarrow f=30\,cm$