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 find the angle between the reflected and transmitted rays, we can use the law of reflection and the law of 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 will also be 45°.
The law of refraction, also known as Snell's law, relates the angles of incidence and refraction to the indices of refraction of the two mediums. Snell's law is given by:
n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
where n1 and n2 are the respective indices of refraction of the incident and transmitting medium.
In this case, the incident medium is air, which has an index of refraction of approximately 1.00, and the transmitting medium is glass with an index of refraction of 1.50.
Using Snell's law, we can solve for the angle of refraction.
sin(45°) = (1.50 * sin(angle of refraction)) / 1.00
Multiplying both sides of the equation by 1.00 and dividing both sides by 1.50, we get:
sin(45°) / 1.50 = sin(angle of refraction)
Using a calculator, we find that sin(45°) / 1.50 ≈ 0.469
To find the angle of refraction, we take the arcsine of both sides of the equation:
angle of refraction ≈ arcsin(0.469)
Using a calculator again, we find that the angle of refraction is approximately 28.3°.
Therefore, the angle between the reflected and transmitted rays will be the difference between the angle of incidence and the angle of refraction:
angle between rays = 45° - 28.3° ≈ 16.7°
So, the angle between the reflected and transmitted rays is approximately 16.7°.