# The thickness at the centre of a plano convex lens

Question:

The thickness at the centre of a plano convex lens is $3 \mathrm{~mm}$ and the diameter is $6 \mathrm{~cm}$. If the speed of light in the material of the lens is $2 \times 10^{8} \mathrm{~ms}^{-1}$. The focal length of the lens is

$2 \times 10^{8} \mathrm{~ms}^{-1}$. The focal length of the lens is

1. $0.30 \mathrm{~cm}$

2. $15 \mathrm{~cm}$

3. $1.5 \mathrm{~cm}$

4. $30 \mathrm{~cm}$

Correct Option: , 4

Solution:

(4)

$\mathrm{R}^{2}=\mathrm{r}^{2}+(\mathrm{R}-\mathrm{t})^{2}$

$\mathrm{R}^{2}=\mathrm{r}^{2}+\mathrm{R}^{2}+\mathrm{t}^{2}-2 \mathrm{Rt}$

Neglecting $t^{2}$, we get

$\mathrm{R}=\frac{\mathrm{r}^{2}}{2 \mathrm{t}}$

$\therefore \frac{1}{\mathrm{f}}=(\mu-1)\left(\frac{1}{\mathrm{R}}-\frac{1}{\infty}\right)=\frac{\mu-1}{\mathrm{R}}$

$\mathrm{f}=\frac{\mathrm{R}}{\mu-1}=\frac{\mathrm{r}^{2}}{2 \mathrm{t}(\mu-1)}=\frac{\left(3 \times 10^{-2}\right)^{2}}{2 \times 3 \times 10^{-3} \times\left(\frac{3}{2}-1\right)}$

$=\frac{9 \times 10^{-4}}{6 \times 10^{-3} \times 1} \times 2$

$\mathrm{f}=0.3 \mathrm{~m}=30 \mathrm{~cm}$