Question

The speed of light in media 'A' and 'B' are 2.0 × 10¹⁰ cm/s and 1.5 × 10¹⁰ cm/s respectively. A ray of light enters from medium B to A at an incident angle 'θ'. If the ray suffers total internal reflection, then ______.

विकल्प

• `theta = sin^-1(3/4)`

• `theta > sin^-1(3/4)`

• `theta < sin^-1(3/4)`

• `theta > sin^-1(3/4)`

Answer 1

The speed of light in media 'A' and 'B' are 2.0 × 10¹⁰ cm/s and 1.5 × 10¹⁰ cm/s respectively. A ray of light enters from medium B to A at an incident angle 'θ'. If the ray suffers total internal reflection, then `bbunderline(theta > sin^-1(3/4))`.

Explanation:

As, `mu = c/v`

Hence, `mu_A = c/v_A = (3 xx 10^8)/(2.0 xx 10^8) = 1.5`

Similarly, `mu_B = c/v_B = (3 xx 10^8)/(1.5 xx 10^8) = 2`

TIR occurs when the angle of incidence is greater than the critical angle, i.e., θ > i_C.

Now, μ_B sin i_C = μ_A sin90˚

`2sin i_C = 1.5 xx 1`

`sini_C = 1.5/2`

`i_C = sin^-1(1.5/2) = sin^-1(3/4)`

Hence, `theta > sin^-1(3/4)`