Question

For a plane convex lens $(\mu =1.5)$ having radius of curvature $10cm$. It is silvered on its plane surface. Find focal length after silvering.

• A. $10cm$
• B. $20cm$
• C. $15cm$
• D. $25cm$

Answer 1

The correct option is B

$20cm$

Step 1: Given

Refractive Index $\mu =1.5$

Radius of curvature $R_1=10cm$

The radius of curvature of the plane surface $R_2=\infty$

Step 2: Find the focal length

The focal length is given by the Lens Maker formula.

$$\begin{gathered} \frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_{\infty }}) \\ \frac{1}{f}=(1.5-1)(\frac{1}{10}-\frac{1}{\infty }) \\ \frac{1}{f}=(0.5)\frac{1}{10} \\ \Rightarrow f=20cm \end{gathered}$$

Hence, option B is the correct option.