Question

Let \( \mu_1 \) and \( \mu_2 \) be the refractive indices of two media. \( v_1 \) and \( v_2 \) are the velocities of light in the media respectively. Which one of the following relations is TRUE?

• A. \( \mu_1 v_1 = \mu_2 v_2 \)
• B. \( \mu_2 v_1 = \mu_1 v_2 \)
• C. \( \mu_1 v_1^2 = \mu_2 v_2^2 \)
• D. \( \mu_2^2 v_1 = \mu_1^2 v_2 \)

Hint:

The refractive index and the velocity of light are inversely related. In different media, this relationship holds: \( \mu_1 v_1 = \mu_2 v_2 \).

Answer 1

The Correct Option is A

Step 1: Using the relationship between refractive index and velocity.
The refractive index \( \mu \) is related to the speed of light \( v \) in a medium by the equation: \[ \mu = \frac{c}{v} \] Where \( c \) is the speed of light in vacuum. Thus, for two media: \[ \mu_1 v_1 = \mu_2 v_2 \] This is the correct relationship. Therefore, the correct answer is (A) \( \mu_1 v_1 = \mu_2 v_2 \).