The diagram given below shows a triangular prism of a certain material with fluorescent screen placed adjacent to it. The yellow light ray striking the surface ST of the prism shows a fluorescent spot at point X.

(a) Calculate the critical angle of the material of the prism for yellow colour.

(b) To move the fluorescent spot towards Y, the value of θ should be …………… [> 50, < 50 or = 50].

(c) Which direction will the florescent spot move if yellow light is replaced with indigo light? (towards Y or towards Z)

(a) As, the ray emerges via ST then it's angle of refraction with the normal is 90° and since, critical angle is the angle of incidence in the denser medium corresponding to which the angle of refraction in the rarer medium is 90° so here, angle of incidence is at critical angle.

Now,

From the diagram,

θ = 50°

Then,

Angle of incidence of the yellow ray = 90° - 50° = 40°

Hence, critical angle of the material of the prism for yellow colour is 40°.

(b) To move the fluorescent spot towards Y, the value of θ should be > 50.

Reason—

Case 1 : When θ is equal to 50°, the ray strikes at X which is the present case.

Case 2 : When θ is less than 50°, the incident angle becomes greater than the critical angle i.e., 40° so light will reflect at the surface ST and hence move toward Z depending upon the value of θ but will never move towards Y as shown below.

Case 3 : When θ is greater than 50°, the incident angle becomes less than the critical angle i.e., 40° so no total internal reflection takes place and light will suffer refraction at the surface ST and hence move toward Y depending upon the value of θ as shown below.

(c) Towards Z

Reason— The critical angle increases with increase in the wavelength of light. Since indigo light has a shorter wavelength than yellow light, its critical angle is less than 40°. Here, the angle of incidence at ST is 50°, which is greater than the critical angle. Therefore, the indigo light will undergo total internal reflection at ST and travel towards Z, as shown below.