Question

A ray of light travelling through rarer medium is incident at a very small angle \( \theta \) on a glass slab and after refraction its velocity is reduced by 20%. The angle of deviation is

• A. \( \frac{\theta}{5} \)
• B. \( \frac{\theta}{4} \)
• C. \( \frac{\theta}{2} \)
• D. \( \frac{\theta}{3} \)

Hint:

When light passes from one medium to another and its velocity is reduced, the angle of deviation changes. The reduction in velocity leads to a decrease in the angle of deviation.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Refraction causes a change in velocity and direction. The refractive index is related to the ratio of velocities in the two media.
Step 2: Key Formula or Approach:
1. Refractive index \( \mu = \frac{v_1}{v_2} \).
2. Snell's Law for small angles: \( \mu = \frac{i}{r} \).
3. Deviation \( \delta = i - r \).
Step 3: Detailed Explanation:
Let the initial velocity be \( v \). The reduced velocity is \( v - 20% \text{ of } v = 0.8v \).
So, \( \mu = \frac{v}{0.8v} = \frac{10}{8} = \frac{5}{4} \).
Using Snell's Law for small angle \( i \):
\[ \mu = \frac{i}{r} \Rightarrow \frac{5}{4} = \frac{i}{r} \Rightarrow r = \frac{4i}{5} \]
The angle of deviation is:
\[ \delta = i - r = i - \frac{4i}{5} = \frac{i}{5} \]
Step 4: Final Answer:
The angle of deviation is \( i/5 \).