Question

The velocity of light in transparent media A and B separated by a plane boundary are 2.0 × 10⁸ and 2.5 × 10⁸ ms⁻¹ respectively. The critical angle for a light ray passing from A to B at the boundary is ______.

Options

• `sin^-1 (1/2)`

• `sin^-1 (2/5)`

• `sin^-1 (4/7)`

• `sin^-1 (4/5)`

Answer 1

The critical angle for a light ray passing from A to B at the boundary is `bbunderline(sin^-1 (4/5))`.

Explanation:

Given:

Velocity of light in medium A (v_A) = 2.0 × 10⁸ m/s

Velocity of light in medium B (v_B) = 2.5 × 10⁸ m/s

Light is going from medium A to B.

Step 1: Refractive index:

Refractive index nnn is inversely proportional to the speed of light in the medium:

`n_B/n_A = v_A/v_B`

= `(2.0 xx 10^8)/(2.5 xx 10^8)`

= `2/2.5`

= `4/5`

Step 2: Critical angle formula:

Critical angle θ_c​ (from denser to rarer):

`sin θ_c = n_B/n_A`

`sin θ_c = 4/5`

`θ_c = sin^-1 (4/5)`