In the adjacent diagram, AO is a ray of light incident on a rectangular glass slab.

(a) Complete the path of the ray until it emerges out of the slab.

(b) In the diagram, mark the angle of incidence (i) and the angle of refraction (r) at the first interface. How is the refractive index of glass related to angles i and r?

(c) Mark angle of emergence by the letter e. How are the angles i and e related?

(d) Which two rays are parallel to each other? Name them.

(e) Indicate in the diagram the lateral displacement between the emergent ray and the incident ray. State one factor that affects the lateral displacement.

(a) The below diagram shows the path of the ray until it emerges out of the slab:

(b) In diagram, the angle of incidence (i) and the angle of refraction (r) are marked.

Refractive index of glass μ is related to the angle of incidence (i) and angle of reflection (r) by Snell's second law and is represented as —

The ratio of the sine of the angle of incidence i to the sine of the angle of refraction r is constant for the pair of given media

$\dfrac{\text{sin i}}{\text{sin r}} = \text{constant }$1\mu2 \\[0.5em]

The constant ₁μ₂ is called the refractive index of the second medium with respect to the first medium.

(c) The angle of emergence (e) is marked in diagram.

As the refraction occurs at two parallel surfaces PQ and RS, therefore angle MOB = angle N₁BO and by the principle of reversibility of the path of a light ray angle of emergence (e) is equal to the angle of incidence (i).

(d) As the refraction occurs at two parallel surfaces PQ and RS, therefore angle MOB = angle N₁BO and by the principle of reversibility of the path of a light ray angle of emergence (e) is equal to the angle of incidence (i).

Hence, the emergent ray BC is parallel to the incident ray AO.

(e) The lateral displacement between the incident ray and the emergent ray is represented by XY.

One of the factors that affects lateral displacement is the the thickness of the medium. More the thickness of the medium more is the lateral displacement.