A beam of light is incident upon a flat piece of glass (n = 1.50) at an angle of incidence of 45°. Part of the beam is transmitted and part is reflected. What is the angle between the reflected and transmitted rays?

To determine the angle between the reflected and transmitted rays, we can use the laws of reflection and refraction.

The law of reflection states that the angle of incidence is equal to the angle of reflection. In this case, the angle of incidence is 45°, so the angle of reflection is also 45°.

The law of refraction, also known as Snell's law, relates the angles and indices of refraction of the incident and transmitted rays. It is given by:

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

where:
- n1 is the refractive index of the medium the incident ray is coming from (in this case, air - approximately 1.00)
- theta1 is the angle of incidence
- n2 is the refractive index of the medium the transmitted ray is entering (in this case, glass - 1.50)
- theta2 is the angle of refraction

We can rearrange the equation to solve for the angle of refraction, theta2:

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

Substituting the given values:
- n1 = 1.00 (refractive index of air)
- theta1 = 45° (angle of incidence)
- n2 = 1.50 (refractive index of glass)

theta2 = arcsin((1.00 * sin(45°)) / 1.50)

Now, let's calculate the value of theta2 using a scientific calculator:

theta2 = arcsin(0.707 / 1.50) ≈ 33.8°

Therefore, the angle between the reflected and transmitted rays is approximately 33.8°.