Question

A ray of light falls normally on the face of a glass prism (n = 1.5). Find the angle of the prism if the ray just fails to emerge from the second face.

Answer 1

Given:

Refractive index of glass, n = 1.5

Ray falls normally on the first face (so it goes undeviated)

The ray just fails to emerge from the second face (i.e., total internal reflection occurs).

To Find:

Angle of the prism A

Concept used:

When a ray falls normally on one face and just fails to emerge from the second face, the angle of incidence at the second face equals the critical angle.

From prism geometry:

Angle of incidence at second face = A

At the point of total internal reflection:

A = C (critical angle)

Calculation:

Now, using the formula:

sin C = `1/n`

sin C = `1/1.5`

sin C = 0.6667

C = sin⁻¹ (0.6667)

C ≈ 41.8°