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:

Find the refractive index from the reduction in speed, and use small angle approximations in Snell's law.

Answer 1

The Correct Option is A

Step 1: Index
$n=\dfrac{1}{1-0.2}=1.25$

Step 2: Refraction angle
$r=\dfrac{\theta}{1.25}=0.8\theta$

Step 3: Deviation
$\theta-0.8\theta=0.2\theta=\dfrac{\theta}{5}$.

Final Answer:
The deviation is $\theta/5$. \[ \boxed{\text{(A) }\dfrac{\theta}{5}} \]