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…

(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.