Refraction of Light in Diamond: Understanding Angles

What is the angle of refraction inside the diamond?

Light in air enters a diamond at an angle of incidence of 48.0 degrees. What is the angle of refraction inside the diamond?

A. 19.8

B. 24.78

C. 45.6

D. 17.98

Angle of Refraction Calculation

The angle of refraction inside the diamond can be calculated using Snell's Law and the refractive indices of the two mediums involved.

When light passes from one medium to another, such as from air to a diamond, it undergoes refraction. The change in direction of light is determined by Snell's Law, which relates the angles and the refractive indices of the two mediums.

In this case, the angle of incidence is given as 48.0 degrees, and the refractive index of diamond is 2.42. By applying Snell's Law and rearranging the formula, we can determine the angle of refraction inside the diamond.

Calculating the Angle of Refraction:

Given:
Angle of Incidence (θ₁) = 48.0°
Refractive Index of Diamond (n₂) = 2.42

Using Snell's Law:
n₁ × sin(θ₁) = n₂ × sin(θ₂)

Plugging in the values:
sin(θ₂) = (1 / 2.42) × sin(48.0°)
sin(θ₂) ≈ 0.413 × 0.743
sin(θ₂) ≈ 0.307

Calculating the angle:
θ₂ ≈ sin⁻¹(0.307)
θ₂ ≈ 17.98°

Therefore, the angle of refraction inside the diamond is approximately 17.98 degrees, matching option D in the given choices.