a ray of light is incident at an angle'a' at a boundary separating two transparent media. Light is transmitted.However if the angle of incidence is increased very slightly ,the ray gets refracted into the incident medium.The difference between the angles by which the incident light is deviated in the first case and that in the second case is A)2'a' B)90(degrees)-'a' C)180(degrees)-'a' D)180(degrees)-2'a'

To tackle this question, we need to delve into the principles of refraction and how light behaves at the boundary between two different media. When light travels from one medium to another, its speed changes, which causes it to bend or refract. The angle at which the light hits the boundary is known as the angle of incidence, denoted as 'a'. Let's break down the scenario you've presented.

Understanding Refraction

When light moves from a medium with a certain refractive index to another medium with a different refractive index, it bends according to Snell's Law, which states:

n1 * sin(a) = n2 * sin(b)

Here, 'n1' and 'n2' are the refractive indices of the two media, 'a' is the angle of incidence, and 'b' is the angle of refraction. If the angle of incidence is increased slightly, the behavior of the light changes significantly.

Analyzing the Situation

In your scenario, when the angle of incidence 'a' is increased slightly, the light ray that was previously refracted into the second medium now starts to refract back into the first medium. This phenomenon occurs due to the critical angle, which is the angle of incidence beyond which light cannot pass into the second medium and is instead reflected back into the first medium.

Calculating the Deviation

Let’s denote the new angle of incidence as 'a + Δa', where 'Δa' is a very small increase in the angle. The deviation of the light ray can be understood as the difference between the angles of refraction in both cases:

• In the first case, the light is transmitted into the second medium at an angle 'b'.
• In the second case, when the angle of incidence is increased, the light refracts back into the first medium, which we can denote as angle 'b' (but in the opposite direction).

The key here is to recognize that the total deviation caused by the change in angle is related to how much the angle of incidence has changed. The deviation can be expressed as:

Deviation = (b - 0) + (0 - (90° - b)) = b + (b - 90°) = 2b - 90°

Finding the Correct Answer

Since we know that the angle of refraction 'b' is related to the angle of incidence 'a', we can express the deviation in terms of 'a'. When the angle of incidence is increased slightly, the deviation can be approximated as:

Deviation = 180° - 2a

This means that the difference between the angles by which the incident light is deviated in the first case and the second case is:

180° - 2a

Final Thoughts

Thus, the correct answer to your question is D) 180(degrees) - 2a. This reflects how the light behaves at the boundary when the angle of incidence is slightly increased, leading to a significant change in the path of the light ray.