To find the critical angle for the glass-air surface, we need to use Snell's law, which relates the angles of incidence and refraction when light travels from one medium to another.
Snell's law is given by:
n₁sinθ₁ = n₂sinθ₂
Where: n₁ is the refractive index of the first medium (air), θ₁ is the angle of incidence, n₂ is the refractive index of the second medium (glass), θ₂ is the angle of refraction.
In this case, the light is incident from air to glass, and we are given the angle of incidence (θ₁) as 45 degrees and the angle of refraction (θ₂) as 15 degrees.
To find the critical angle, we need to determine the angle of incidence that corresponds to the angle of refraction of 90 degrees (light being refracted along the interface).
When the angle of refraction is 90 degrees, sinθ₂ equals 1. Therefore, we can rewrite Snell's law as:
n₁sinθ₁ = n₂
To find the critical angle, we need to determine the angle of incidence (θ₁) that satisfies this equation. Rearranging the equation gives us:
θ₁ = arcsin(n₂/n₁)
Substituting the refractive indices, we can calculate the critical angle:
θ₁ = arcsin(n₂/n₁) = arcsin(1.50/1.00) = arcsin(1.50)
Using a calculator, we find that the arcsine of 1.50 is approximately 90 degrees. Therefore, the critical angle for the glass-air interface is 90 degrees.
Note: The critical angle is the angle of incidence at which the angle of refraction becomes 90 degrees, and light is refracted along the interface. If the angle of incidence exceeds the critical angle, total internal reflection occurs, and the light is reflected back into the original medium (in this case, air).