Question

Light is moving through a sample of acrylic plastic (n = 1.49). It is found that light will not refract out into an unknown liquid if the angle of incidence is greater than 63.2 degrees. What is the index of refraction of the unknown?

Answer Choices,
1.49
1.33
1.57
1.75

Answer 1

Answer: B or 1.33

Explanation:

In this case, the angle of incidence (θ₁) is given as 63.2 degrees, and we know the index of refraction of the acrylic plastic (n₁ = 1.49).

Using Snell's Law, we can rearrange the equation to solve for n₂:

n₂ = (n₁sinθ₁) / sinθ₂

Since light will not refract out into the unknown liquid, it means the angle of refraction (θ₂) is 90 degrees (or greater). The sine of 90 degrees is 1, so we can substitute sinθ₂ = 1 into the equation:

n₂ = (n₁sinθ₁) / 1 = n₁sinθ₁

Plugging in the values, we have:

n₂ = 1.49 * sin(63.2 degrees) ≈ 1.333

Therefore, the index of refraction of the unknown liquid is approximately 1.333.

The closest answer choice is 1.33.