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: Understanding the Concept
Speed is reduced by 20 percent, so \(v=0.8c\) and the refractive index of glass is \(n=\dfrac{c}{v}=\dfrac{1}{0.8}=\dfrac54\).

Step 2: Snell's law
\(\sin i=n\sin r\). For small angles, \(i=nr\), so \(r=\dfrac{4}{5}\theta\).

Step 3: Deviation
\(\delta=i-r=\theta-\dfrac45\theta=\dfrac{\theta}{5}\)

Step 4: Compare the options
The first option, \(\dfrac{\theta}{5}\), is correct.

Final Answer:
The angle of deviation is one-fifth of the angle of incidence. \[ \boxed{\text{(A) }\dfrac{\theta}{5}} \]