Question

Formula used when a light ray enters a medium of refractive index n₂ from a medium of refractive index n₁ at curved surface with radius of curvature R is

• A. \(\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}\)
• B. \(v-u = \frac{n_2 - n_1}{R}\)
• C. \(\frac{v}{n_2} - \frac{u}{n_1} = \frac{n_2 - n_1}{R}\)
• D. \(\frac{n_2}{v}+\frac{n_1}{u} = \frac{n_2 - n_1}{R}\)

Answer 1

The Correct Option is A

To solve this problem, we need to recall the formula used for refraction at a spherical surface separating two media of different refractive indices.

1. Refraction at Spherical Surface:
When a light ray travels from a medium of refractive index \( n_1 \) to another medium with refractive index \( n_2 \), and the interface is a curved surface of radius \( R \), the refraction formula is:

\( \frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R} \)

2. Meaning of Symbols:
- \( u \): object distance
- \( v \): image distance
- \( R \): radius of curvature
- \( n_1 \): refractive index of medium where object is located
- \( n_2 \): refractive index of the second medium

3. Evaluating the Options:

(1) \( \frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R} \) – Correct ✅

(2) \( v - u = \frac{n_2 - n_1}{R} \) – Incorrect (dimensionally inconsistent)

(3) \( \frac{v}{n_2} - \frac{u}{n_1} = \frac{n_2 - n_1}{R} \) – Incorrect

(4) \( \frac{n_2}{v} + \frac{n_1}{u} = \frac{n_2 - n_1}{R} \) – Incorrect (wrong sign)

Final Answer:
The correct option is (A).