A prism, made of glass of refractive index 1.50, has two plane faces at an angle 33 to each other. A ray of light enters the glass from one side perpendicular to that face and emerges through the other.
Part A:
As the ray enters the glass, what is its angle of incidence ?
Give your answer in degrees.
PartB:
Just before the ray emerges from the glass, what is its angle of incidence ?
Give your answer in degrees.
Part C:
If the prism is in air calculate the deviation of the ray.
Give your answer in degrees. Remember, you're being asked for the deviation angle, not the angle of refraction. The deviation angle is the difference between the incidence and refraction angles at the glass/air interface.
Learn Snell's law and make a serious attempt on your own. We are not going to do all of these for you.
A: an angle of incidence is zero because this is the angle between the normal to the surface and the incident ray.
B: examine the triangle formed by: the point where the ray enters the prism, the vertex of triangle (33o) and the point where the ray emerges from the prism. β = 180o - 90o - 33o=57o. This is the angle between the ray propagating in the prism and the second plane face of prism, therefore, the second angle of incidence is 33o.
C: sin r/sin i1=1.5, sin r = 1.5•sin i1=0.817,
r = 54.8o.
deviation is 57o-54.8o=2.2o
To answer these questions, we need to understand Snell's Law, which relates the angles of incidence and refraction when light passes through a boundary between two different media.
Snell's Law states: n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
Part A:
Since the ray of light is perpendicular to the face of the prism, the angle of incidence is 0 degrees.
Part B:
To find the angle of incidence just before the ray emerges from the glass, we need to determine the angle of refraction first. Since the light is passing from a denser medium (glass) to a less dense medium (air), the angle of refraction will be larger than the angle of incidence. We will use Snell's Law to find the angle of refraction, and then subtract it from 90 degrees to get the angle of incidence.
1. Calculate the angle of refraction:
n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
1.50 * sin(0 degrees) = 1.00 * sin(angle of refraction)
sin(angle of refraction) = 0
angle of refraction = 0 degrees
2. Calculate the angle of incidence just before the ray emerges:
angle of incidence = 90 degrees - angle of refraction
angle of incidence = 90 degrees - 0 degrees
angle of incidence = 90 degrees
Part C:
To calculate the deviation angle, we need to find the angle of refraction at the glass/air interface and subtract the angle of incidence.
1. Calculate the angle of refraction at the glass/air interface:
n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
1.00 * sin(90 degrees) = 1.50 * sin(angle of refraction)
sin(angle of refraction) = 0.67
angle of refraction = arcsin(0.67) (use inverse sine function)
2. Calculate the deviation angle:
deviation angle = angle of refraction - angle of incidence
deviation angle = arcsin(0.67) - 0 degrees
deviation angle = arcsin(0.67) degrees
Therefore, the deviation angle of the ray in air is approximately equal to the arcsin(0.67) degrees.