If the critical angle for light at an interface between certain substances is 54.2 degrees, what is the polarizing angle at this same interface?
I am confused!
my book says the answer is 39 degrees..
Right.
arctan N2/N1 = arctan 0.81106 = 39.0 degrees
I failed to use the formula correctly
I can help you understand how to find the polarizing angle at this interface. First, let's clarify what the polarizing angle is. The polarizing angle is the angle of incidence at which the reflected light becomes completely polarized (having vibrations oscillating in a single plane).
To find the polarizing angle at the interface, you need to apply Snell's law and the concept of total internal reflection. Here are the steps you can follow:
1. Recall Snell's law: n₁sinθ₁ = n₂sinθ₂, where n₁ and n₂ are the refractive indices of the substances, and θ₁ and θ₂ are the angles of incidence and refraction, respectively.
2. At the critical angle, the angle of refraction θ₂ is 90 degrees, which means the refracted ray travels parallel to the interface.
3. To determine the polarizing angle, we need to find the angle of incidence (θ₁) that corresponds to a refracted angle of 90 degrees.
4. Rearrange Snell's law to solve for sinθ₁: sinθ₁ = (n₂/n₁)sinθ₂.
5. Plug in the known values: n₂/n₁ = 1 (since the refractive index of air is considered 1), and sinθ₂ = sin(90°) = 1.
6. Solve for sinθ₁: sinθ₁ = 1.
7. To find the polarizing angle, take the inverse sine (sin⁻¹) of both sides: θ₁ = sin⁻¹(1).
Remember that the inverse sine function returns the angle in radians. Converting radians to degrees, we find that sin⁻¹(1) = 90°.
Therefore, the polarizing angle at this interface would be 90 degrees.
I hope this explanation helps clarify the concept of the polarizing angle for you!
Use the critical angle to get the index of refraction ratio, N1/N2
Sin 54.2 = N2/N1 = 0.81106
N1/N2 = 1.233
For the polarizing (Brewster) angle, A
tan A = N2/N1
N2/N1 = 50.1 degrees
See http://en.wikipedia.org/wiki/Brewster's_angle
for detailed explanation