A ray of light traveling in air strikes the midpoint of one face of an equiangular glass prism (n = 1.50) at an angle of exactly 30 degrees. a)Trace the path of the light ray through the glass, and find the angle of incidence of the ray at the bottom of the prism. b) Will the ray pass through the bottom surface of the prism or will it be totally internally reflected?

79.3

To trace the path of the light ray through the glass prism and find the angle of incidence at the bottom of the prism, we need to use Snell's law.

a) Snell's law relates the angles of incidence and refraction with the refractive indices of the media involved. The equation is given as:

n1 * sin(theta1) = n2 * sin(theta2)

Where:
- n1 = index of refraction of the medium before the boundary
- n2 = index of refraction of the medium after the boundary
- theta1 = angle of incidence
- theta2 = angle of refraction

Given:
- n1 = 1 (refractive index of air)
- n2 = 1.50 (refractive index of the glass prism)
- theta1 = 30 degrees

First, we need to find the angle of refraction, theta2. Rearranging Snell's law equation, we have:

sin(theta2) = (n1 / n2) * sin(theta1)
sin(theta2) = (1 / 1.50) * sin(30)
sin(theta2) = 0.666 * 0.5
sin(theta2) = 0.333 or approximately 0.33

Using the inverse sine function, we find:
theta2 = sin^(-1)(0.333)
theta2 = 19.5 degrees (approximately)

Now, since the prism is equiangular, the angle at the bottom of the prism is also 30 degrees. Therefore, the angle of incidence at the bottom of the prism is 30 degrees.

b) To determine if the ray will pass through the bottom surface or be totally internally reflected, we need to compare the angle of incidence (30 degrees) to the critical angle.

The critical angle is the angle of incidence that causes a refracted ray to be at an angle of 90 degrees, known as the angle of refraction. It is given by:

critical angle = sin^(-1)(n2 / n1)

critical angle = sin^(-1)(1.50 / 1)
critical angle = sin^(-1)(1.50)

Using a calculator, we find:
critical angle ≈ 41.8 degrees

Since the angle of incidence (30 degrees) is less than the critical angle (41.8 degrees), the ray will pass through the bottom surface of the prism instead of being totally internally reflected.

You need to post some work. I will be happy to critique your thinking.