Question

A glass prism of refractive index 1.5 is immersed in water `("refractive index" = 4/3)`. A light beam is incident normally on the face AB. It will be totally reflected at the face AC to reach the face BC, if:

Options

• `sin θ > 8/9`

• `2/ 3 < sin θ < 8/9`

• `sin θ < 2/3`

• none of these

Answer 1

`bb(sin θ > 8/9)`

Explanation:

For the prism to totally internally reflect light at face AC, the incident angle at AC must be greater than the critical angle. Given the refractive index of the glass prism (n₁ = 1.5) and water `(n_2 = 4/3)`, the critical angle condition gives `sin θ > n_2/n_1 = (4/3)/1.5 = 8/9`. Hence, total internal reflection occurs if `sin θ > 8/9`.