Define lateral displacement of light. Give the formula to find the refractive index of the glass slab in terms of angle of incidence and angle of refraction.

Lateral displacement of light refers to the horizontal shift experienced by a light ray when it passes through a transparent medium, such as a glass slab, at an angle other than perpendicular to the surface.

The formula to find the lateral displacement (d) of light passing through a glass slab can be given as:

d = t * tan(θ)

where:

d is the lateral displacement of the light ray,
t is the thickness of the glass slab, and
θ is the angle of incidence of the light ray.
Now, let's move on to the formula for calculating the refractive index of the glass slab using the angle of incidence (θ₁) and the angle of refraction (θ₂).

The formula is based on Snell's law, which states:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

where:

n₁ is the refractive index of the medium the light ray is coming from (usually air or vacuum),
n₂ is the refractive index of the glass slab, and
θ₁ and θ₂ are the angles of incidence and refraction, respectively.
To express the refractive index of the glass slab (n₂) in terms of θ₁ and θ₂, we can rearrange Snell's law as follows:

n₂ = n₁ * sin(θ₁) / sin(θ₂)

This formula allows you to calculate the refractive index of the glass slab when the angles of incidence and refraction are known, along with the refractive index of the medium the light is coming from.