Question

A light ray coming from the Sun falls on the water surface from air at an angle of 45° as shown. If the ray got refracted by 30° on passing through the air-water interface, then calculate:

i. Refractive index of water

ii. Speed of light inside water

Answer 1

The refractive index of water is 1.414, and the speed of light in water is approximately 2.121 x 10^8 m/s.

Step-by-step explanation:

To calculate the refractive index of water, we can use the formula:

Refractive index = sin(angle of incidence) / sin(angle of refraction)

Given that the incident angle is 45° and the angle of refraction is 30°, we can plug these values into the formula and calculate:

Refractive index = sin(45°) / sin(30°) = 0.707 / 0.5 = 1.414

Therefore, the refractive index of water is 1.414.

To calculate the speed of light inside water, we can use the formula:

Speed of light in a medium = Speed of light in vacuum / Refractive index of the medium

Since the speed of light in vacuum is approximately 3 x 10^8 m/s, and the refractive index of water is 1.414, we can calculate:

Speed of light in water = 3 x 10^8 m/s / 1.414 = 2.121 x 10^8 m/s