Question

(a) Draw and label the diagram given:

(i) Incident ray
(ii) Refracted ray
(iii) Emergent ray
(iv) Angle of refraction
(v) Angle of deviation
(vi) Angle of emergence.
(b) The refractive index of diamonds is 2.42. What is the meaning of this statement in relation to the speed of light?

Answer 1

Hint: First we can label the given diagram and discuss the terms briefly. The given diagram has a prism in which refraction takes place, as there are two surfaces of the prism there is extra term emergent ray and the angle of emergent which we will discuss while labeling. Secondly, we will discuss the refractive index and what the quantity tells us.

Complete step-by-step solution:
(a) The diagram we have is of prism and prism has two surfaces through which light passes. The first surface is AB and the second surface is AC. The labeled diagram is given as

(i) Incident ray is the ray which is incident on the plane of the surface, here on the plane AB the light ray which is incident on it is PQ. The line NN’ is normal for the surface AB.
(ii) Refracted ray is the ray which gets deviated (or refracted) from its path due to change in medium, it can either bend towards the normal or away from normal. Here it bends towards the normal, QR is the refracted ray.
(iii) Emergent ray is the ray, which comes out of the refracting surface, where the surface is AC and the ray RS is the emergent ray.
(iv) Angle of refraction is the angle, which refracted ray makes with respect to the normal. Here normal is NN’ and the refracted ray is QR while r is the angle which the ray QR is making with respect to NN’. Hence r is the angle of refraction.
(v) Angle of deviation is the difference between the angle of incidence and angle of refraction but for prism, it is different in angle of incidence and angle of emergent because in prism the ray deviates twice. QGH is the extended line of the incident ray and GR is the extended line for emergent ray and the angle which both the line makes i.e. d is the angle of deviation.
(vi) Angle of emergent is the angle which emergent ray makes with the normal. Here emergent ray is RS, normal is MM’, and e is the angle of emergence.
(b) Refractive index of an object tells us the change in the speed of light when the light ray travels from one medium to another. Here the object is diamond which has a refractive index of 2.42, hence the light ray passing from the vacuum to the diamond it slows down with the factor of 2.42 and i.e. the speed of light within the diamond will be \[\dfrac{1}{2.42}\] times of the speed of light.

Note: The angle of the incident is also labeled in the above diagram shown as i. The angle of incidence is the angle, which incident ray makes with respect to normal.
The speed of light is constant but it can slow down if it travels from rarer to denser medium and it can’t have a value greater than c which is the speed of light in a vacuum.