Question

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

• A. $15\text{cm}$
• B. $30\text{cm}$
• C. $20\text{cm}$
• D. $10\text{cm}$

Answer 1

The correct option is B $30\text{cm}$

Given: $d=3\text{cm},t=0.3\text{cm},v_{medium}=2\times {10}^8\text{m/s}$


$\mu =\frac{\text{velocity of light in vacuum}}{\text{velocity of light in medium}}=\frac{3}{2}$

And, $R^2=d^2+(R-t{)}^2$

$\Rightarrow R^2-d^2=R^2(1-\frac{t}{R}{)}^2$

$\Rightarrow 1-\frac{d^2}{R^2}=1-\frac{2t}{R}=\frac{d^2}{2t}$

$=\frac{3^2}{2\times 0.3}=15\text{cm}$

By using the lens maker’s formula:

$\frac{1}{f}=(\mu -1)\times (\frac{1}{R_1}–\frac{1}{R_2})=(\frac{3}{2}-1)\left(\frac{1}{15}\right)$

$f=30\text{cm}$

Hence, option $\left(C\right)$ is correct.