A light ray enters from glass (n1 = 1.5) to air (n2 = 1.0). Calculate the incident angle at which Θ2 (transmission angle) equals 90 degrees.
and your thinking (with Snells law) is?
You have to assume the angles are measured to the normal.
To calculate the incident angle at which Θ2 (transmission angle) equals 90 degrees, we can use Snell's Law, which relates the incident angle (θ1) and the transmission angle (θ2) to the refractive indices of the two media involved:
n1 * sin(θ1) = n2 * sin(θ2)
Given that n1 = 1.5 and n2 = 1.0 (since air has a refractive index of approximately 1), we want to find the incident angle (θ1) at which the transmission angle (θ2) equals 90 degrees.
When transmission angle (θ2) is 90 degrees, sin(θ2) = 1. Therefore, the equation becomes:
n1 * sin(θ1) = n2 * 1
Since n2 = 1, the equation simplifies to:
n1 * sin(θ1) = 1
To isolate sin(θ1), divide both sides of the equation by n1:
sin(θ1) = 1 / n1
Substituting the value of n1 = 1.5:
sin(θ1) = 1 / 1.5
Now, we can take the inverse sine (sin^(-1)) of both sides to find the incident angle θ1:
θ1 = sin^(-1)(1 / 1.5)
Using a calculator, we can find that θ1 is approximately 41.81 degrees.
Therefore, the incident angle at which the transmission angle θ2 equals 90 degrees is approximately 41.81 degrees.