Assume all angles to be exact.
The critical angle between two materials is 45∘.
If the angle of incidence is 35∘, what is the angle of refraction? (Consider that light can travel to the interface from either material.)
To find the angle of refraction, we can use Snell's law, which relates the angle of incidence (θ₁), the angle of refraction (θ₂), and the refractive indices (n₁ and n₂) of the two materials involved. Snell's law is given by:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Given that the critical angle is 45°, we know that at this angle, the angle of refraction is 90°.
If the angle of incidence is 35°, we need to determine if it is less than or greater than the critical angle. If it is less than the critical angle, the light will be refracted, and if it is greater, the light will be reflected.
Since 35° is less than 45°, the light will be refracted. Therefore, we can use Snell's law to calculate the angle of refraction.
Let's assume that the refractive index of the first material is n₁ and the refractive index of the second material is n₂ (n₁ is the refractive index of the material from which the light is coming, and n₂ is the refractive index of the material into which the light is entering).
For simplicity, let's also assume that the angle of refraction is θ₂.
Snell's law can be written as:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Since we are given the angle of incidence (θ₁) as 35°, and we need to find the angle of refraction (θ₂), we can rearrange the equation as follows:
sin(θ₂) = (n₁ / n₂) * sin(θ₁)
Substituting the values given in the problem, n₁ / n₂ = 1 (since no refractive indices are provided), and θ₁ = 35°, we get:
sin(θ₂) = 1 * sin(35°)
Using a calculator, we can find that sin(35°) ≈ 0.5736.
Taking the inverse sine (sin⁻¹) of both sides of the equation to solve for θ₂, we find:
θ₂ = sin⁻¹(0.5736)
Evaluating this expression using a calculator, we find that θ₂ ≈ 35.13°.
Therefore, the angle of refraction (θ₂) is approximately 35.13°.