A ray of light hits a side of Lucite ( n = 1.5) prism at 50 degree. Assuming that the nearest vertex has an angle of 70 degrees, what is the angle of light that leaves the prism.
There are two possible 50 degree angles of incidence. They are above and below the normal to the face that the ray strikes. You need to be more specific. Only one of the two 50 degree angles of incidence will strike the opposite face. The other strikes the bottom of the prism
In any case, use Snell's law twice.
The angle of refraction inside the prism is given by
sin A = sin50/1.5 = 0.5107
A = 30.7 degrees
Using a bit of geometry, I conclude that the angle of incidence on the second face is 70 - A = 39.3 degrees.
Apply Snell's law again for the final result.
Wait, how did you do that? I understand the part of 30.7 degree, but how did you conclude that the angle of incidence on the second face is 39.3? Could you show the steps, please?
To find the angle of light that leaves the prism, we can use Snell's law, which states:
n1 * sin(theta1) = n2 * sin(theta2)
where:
n1 = refractive index of the medium the light is coming from (in this case, air = 1)
n2 = refractive index of the medium the light is entering (in this case, Lucite = 1.5)
theta1 = angle of incidence
theta2 = angle of refraction (the angle of light that leaves the prism)
Given:
n1 = 1 (refractive index of air)
n2 = 1.5 (refractive index of Lucite)
theta1 = 50 degrees
We need to find theta2.
First, let's convert the angles to radians:
theta1 = 50 degrees * (π/180) = 0.8727 radians
Next, we can rearrange Snell's law to solve for theta2:
sin(theta2) = (n1 / n2) * sin(theta1)
sin(theta2) = (1 / 1.5) * sin(0.8727)
sin(theta2) ≈ 0.6667 * 0.7600
sin(theta2) ≈ 0.5067
Now, we can find theta2 by taking the inverse sine (or arcsine) of both sides:
theta2 ≈ arcsin(0.5067)
Using a scientific calculator or trigonometric table, we can find that:
theta2 ≈ 30.42 degrees
Therefore, the angle of light that leaves the prism is approximately 30.42 degrees.
To solve this problem, we can use Snell's Law, which relates the angles of incidence and refraction for light passing through a boundary between two media.
The formula for Snell's Law is:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
where:
- n₁ is the refractive index of the first medium (in this case, the surrounding medium, usually air, which has a refractive index of approximately 1),
- θ₁ is the angle of incidence,
- n₂ is the refractive index of the second medium (in this case, the Lucite prism, which has a refractive index of 1.5), and
- θ₂ is the angle of refraction.
Given that the angle of incidence, θ₁, is 50 degrees and the refractive index of the prism, n₂, is 1.5, we can rearrange Snell's Law to solve for θ₂.
sin(θ₂) = (n₁ / n₂) * sin(θ₁)
sin(θ₂) = (1 / 1.5) * sin(50)
sin(θ₂) = 0.6667 * 0.7660
sin(θ₂) ≈ 0.511
Now, we can find the angle of refraction, θ₂, by taking the inverse sine (sin⁻¹) of 0.511.
θ₂ = sin⁻¹(0.511)
θ₂ ≈ 30.3 degrees
Therefore, the angle of light that leaves the prism is approximately 30.3 degrees.