Answer:
θ₁ = cos⁻¹ (n₁ / 2n₂)
Explanation:
For this exercise let's use the law of refraction
n₁ sint θ₁ = n₂. sin θ₂
Where n₁ and n₂ are the refractive indices for the two media, θ₁ and θ₂, the angles of incidence and refraction
They tell us that the angle of incidence is equal to the angle refracted over 2
θ₁ = θ₂ / 2
θ₂ = 2 θ₁
Let's replace
n₁ sin θ₁ = n₂ sin θ₂
Let's use the trigonometry relationship
sin 2θ = 2 sinθ cos θ
n₁ sin θ₁ = n₂ (2 sin θ₁ cos θ₁)
n₁ = n₂ cos θ₁
cos θ₁ = n₁ / 2 n₂
θ₁ = cos⁻¹ (n₁ / 2n₂)
Therefore, the angle of incidence is
θ₁ = cos⁻¹ (n₁ / 2n₂)
