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.