Question

The critical angle for a typical glass air interface is $42^\circ$. If a ray of light falls normally on one of the faces of the prism of angle $45^\circ$, the emergent ray will:

• A. Go undeviated
• B. Will undergo refraction with a refracting angle $45^\circ$
• C. Will pass parallel to the second surface
• D. Undergo total internal reflection from the second face

Hint:

Whenever light hits a surface normally ($i = 0^\circ$), it goes completely straight without bending. At the next surface inside a prism, your angle of incidence is always equal to the prism's vertex angle ($i = A$) if the first surface was normal!

Answer 1

The Correct Option is D

Concept: When light passes from a denser medium (glass) to a rarer medium (air), it undergoes Total Internal Reflection (TIR) if the angle of incidence ($i$) inside the denser medium is strictly greater than the critical angle ($C$). If $i = C$, the refracted ray grazes along the boundary surface. If $i < C$, normal refraction occurs.

Step 1: Determine the angle of incidence at the second face.
The ray falls normally on the first surface of the prism, meaning the angle of incidence at the first face is $0^\circ$. Hence, it passes completely undeviated into the prism and strikes the second face (the hypotenuse side). From the geometry of a standard prism with a refracting angle $A = 45^\circ$, the relationship between the internal angles is: \[ r_1 + r_2 = A \] Since the ray enters normally, $r_1 = 0^\circ$. Therefore, the angle of incidence at the second face ($r_2$) is: \[ 0^\circ + r_2 = 45^\circ \implies r_2 = 45^\circ \]

Step 2: Compare the angle of incidence with the critical angle.
We are given that the critical angle $C = 42^\circ$. Comparing the value of the incidence angle at the second boundary ($i = r_2 = 45^\circ$) with the critical angle: \[ 45^\circ > 42^\circ \implies i > C \] Since the angle of incidence is greater than the critical angle, the light ray cannot escape into the air. Instead, it will undergo total internal reflection from the second face.