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 refraction of light.
When a ray of light passes from one medium to another, its speed and direction change due to the difference in refractive indices of the two media. The angle of refraction \( \theta_r \) is related to the angle of incidence \( \theta_i \) by Snell's law:
\[ n_1 \sin \theta_i = n_2 \sin \theta_r, \]
where \( n_1 \) and \( n_2 \) are the refractive indices of the two media.

Step 2: Relating the speed of light in two media.
The refractive index \( n \) is also related to the speed of light in a medium:
\[ n = \frac{c}{v}, \]
where \( c \) is the speed of light in a vacuum and \( v \) is the speed of light in the medium. The problem states that the velocity of light is reduced by 20%, so the new speed \( v' \) is 80% of the original speed:
\[ v' = 0.8v. \]

Step 3: Finding the deviation.
Since the velocity is reduced by 20%, the angle of refraction will be different from what it would be if the light were travelling at the original speed. The angle of deviation \( \delta \) is defined as the difference between the angle of incidence and the angle of refraction:
\[ \delta = \theta_i - \theta_r. \]
Given the relationship between the refractive indices and the speed of light, the deviation is reduced by half due to the 20% decrease in speed.
Final Answer:
Thus, the angle of deviation is:
\[ \boxed{\frac{\theta}{2}}. \]