Question

The thickness at the centre of a planoconvex lens is $3\text{mm}$ and the diameter is $6\text{cm}$. If the speed of light in the material of the lens is $2\times {10}^8{\text{ms}}^{-1}$, the focal length of the lens kept in air is :

• A. $0.30\text{cm}$
• B. $1.5\text{cm}$
• C. $15\text{cm}$
• D. $30\text{cm}$

Answer 1

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


Applying Pythagoras theorem, we have,

$R^2=3^2+{(R-0.3)}^2$

$\Rightarrow R^2=9+R^2+0.09-2\times 0.3R$

$\Rightarrow 0.6R=9.09$

$\Rightarrow R=15.15\text{cm}$

Also,
$\mu =\frac{c}{v}=\frac{3\times {10}^8}{2\times {10}^8}=1.5$

Now, using Lens maker formula,

$\frac{1}{f}=(\mu -1)(\frac{1}{R}-\frac{1}{\infty })$

$\Rightarrow \frac{1}{f}=(1.5-1)\left(\frac{1}{15.15}\right)$

$\Rightarrow f=30.3\text{cm}\approx 30\text{cm}$