show that the ray of light ,on passing through the parallel sided slab of refractive index n, undergoes a lateral displacement.
To show that a ray of light, when passing through a parallel-sided slab of refractive index n, undergoes a lateral displacement, we need to understand the principles of refraction.
1. Introduction to Refraction:
Refraction is the bending of light when it passes from one medium to another, due to the change in its speed. The degree of bending depends on the refractive indices of the two media and the angle at which the light ray strikes the interface.
2. Understanding the Setup:
Consider a parallel-sided slab made of a transparent material, such as glass or acrylic, with a refractive index of n. Let's assume the incident ray of light enters the slab at an angle θ_1 (measured from the normal to the interface) and travels through it.
3. Snell's Law:
Snell's law relates the angles and refractive indices of the incident and refracted rays. It can be stated as: n₁ * sin(θ₁) = n₂ * sin(θ₂), where n₁ and n₂ are the refractive indices of the initial and final media, and θ₁ and θ₂ are the angles of incidence and refraction, respectively.
4. Analyzing the Refraction:
As the incident ray enters the parallel-sided slab, it will refract towards the normal due to the increase in refractive index. Let's designate the angle of refraction inside the slab as θ₂.
Since the slab is parallel-sided, the angle of incidence and refraction at the entry surface will be equal (θ₁ = θ_i). Applying Snell's law, we get: n * sin(θ_i) = n * sin(θ₂).
As the ray exits the slab, it will refract again, but this time away from the normal since the refractive index decreases. The angle of refraction at the exit surface, θₒ, will be larger than θ₂.
5. Lateral Displacement:
To observe lateral displacement, we need to compare the position of the emergent ray with the position of the incident ray.
Since the angles of refraction at both surfaces are different (θ₂ ≠ θₒ), the emergent ray will not be parallel to the incident ray. This non-parallelism results in a lateral displacement.
The magnitude of this lateral displacement can be determined using basic geometry and trigonometry principles.
Thus, we have shown that a ray of light passing through a parallel-sided slab of refractive index n will undergo a lateral displacement due to the change in direction caused by refraction.
Remember, the exact measurements of the displacement will depend on the angle of incidence, refractive index, and thickness of the slab.