Question

diameter of a plano convex lens is 6cm and thickness at the centre is 3mm.if speed of light in material of lens os 2*100000000m/s,the focal length of the lens is?

Answer 1

diameter of a plane convex lens is $6\mathrm{cm}$ and thickness at the centre is $3\mathrm{mm}$. If speed of light in material of lens is $2*100000000\mathrm{m/s}$, the focal length of the lens is?

Solution

Let $R$ be the radius of curvature of the convex surface.

Given that $AB = 3 \, \text{mm} = 0.3 \, \text{cm}$, $AD = \frac{CD}{2} = 3 \, \text{cm}$, refractive index $(n) = 1.5$

By the property of circles,

$$AB = \frac{AD^2}{2R}$$

Therefore, $R = \frac{AD^2}{2AB} = \frac{9}{2 \times 0.3} = 15 \, \text{cm}$

According to thin lens formula,

$$\frac{1}{f} = \frac{n - 1}{R} \rightarrow f = \frac{R}{n - 1} = \frac{15}{1.5 - 1} = 30 \, \text{cm}$$

Answer: $30 \, \text{cm}$.