Question

When a parallel beam of light enters water surface obliquely at some angle, what is the effect on the width of the beam?

Hint:

The width of a light beam reduces when it enters a denser medium at an oblique angle due to the refraction of light.

Answer 1

When a parallel beam of light enters a water surface obliquely, the beam undergoes refraction due to the change in the speed of light when passing from one medium (air) to another (water). Let's break down the effect of this refraction on the width of the beam:

1. Refraction of Light at the Water Surface:

When light passes from air (where the refractive index is approximately 1) into water (with a refractive index of about 1.33), the change in speed causes the light to bend according to Snell's law. The refractive index (\( n \)) is related to the angle of incidence (\( \theta_1 \)) and the angle of refraction (\( \theta_2 \)) as:

\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]

where:

• \( n_1 \) is the refractive index of air (1),
• \( n_2 \) is the refractive index of water (1.33),
• \( \theta_1 \) is the angle of incidence in air, and
• \( \theta_2 \) is the angle of refraction in water.

2. Effect on the Width of the Beam:

When the light enters the water obliquely, the beam bends, causing the light rays to spread out more (or less) depending on the direction of the incident light. Since the speed of light in water is slower, the light rays are refracted towards the normal, causing the beam to become narrower in the direction of propagation.

• As the beam enters the water, the width of the beam decreases due to the bending of the rays towards the normal. This narrowing of the beam occurs because the light slows down in the water, and the rays are closer together after refraction.
• The effect is more pronounced when the angle of incidence is large, as the light bends more sharply towards the normal. For a smaller angle of incidence, the change in the width is less noticeable.

3. Conclusion:

When a parallel beam of light enters the water surface obliquely, the width of the beam decreases due to the refraction of light as it slows down and bends towards the normal. The greater the angle of incidence, the more pronounced the narrowing of the beam.