Question

Focal length of plano-convex lens of refractive index n and radius of curvature R is

• A. f = R
• B. \(f=\frac{R}{2}\)
• C. \(f=\frac{n-1}{R}\)
• D. \(f=\frac{R}{n-1}\)

Answer 1

The Correct Option is D

To solve this question, we need to find the focal length of a plano-convex lens with refractive index \( n \) and radius of curvature \( R \).

1. Lens Maker's Formula:
The general lens maker's formula for focal length \( f \) is:
\[ \frac{1}{f} = (n - 1)\left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]

2. For a Plano-Convex Lens:
- One side is plane \( \Rightarrow R_1 = \infty \)
- One side is convex \( \Rightarrow R_2 = -R \)
Now applying this to the formula:
\[ \frac{1}{f} = (n - 1)\left( \frac{1}{\infty} - \left( -\frac{1}{R} \right) \right) = (n - 1)\left( \frac{1}{R} \right) \]

3. Solving for \( f \):
\[ f = \frac{R}{n - 1} \]

Final Answer:
Option (D) \( f = \frac{R}{n - 1} \) is correct.