Question

The refractive index of a medium ‘x’ with respect to a medium ‘y’ is 2/3 and the refractive index of medium ‘y’ with respect to a medium ‘z’ is 4/3. Find the refractive index of medium ‘z’ with respect to medium ‘x’. If the speed of light in medium ‘x’ is 3 × 10⁸ m/s, calculate the speed of light in medium ‘y’.

Answer 1

The refractive index of medium 'z' with respect to medium 'x' is 2. The speed of light in medium 'y' is 4.5 × 10⁸ m/s.

Step-by-step explanation:

To find the refractive index of medium 'z' with respect to medium 'x', we can use the formula:

nzx = nzy / nxy

Given that the refractive index of medium 'x' with respect to medium 'y' is 2/3 and the refractive index of medium 'y' with respect to medium 'z' is 4/3, we can substitute these values into the formula:

nzx = (4/3) / (2/3) = 2

To calculate the speed of light in medium 'y', we can use the formula:

vy = c / nyx

Given that the speed of light in medium 'x' is 3 × 10⁸ m/s and the refractive index of medium 'y' with respect to medium 'x' is 2/3, we can substitute these values into the formula:

vy = (3 × 10⁸) / (2/3) = 4.5 × 10⁸ m/s