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, which can be represented as:
angle of incidence = angle of reflection
In this case, the angle of incidence is given as 45°, so the angle of reflection will also be 45°.
Now, let's consider the law of refraction. When light passes from one medium to another, the direction of the light wave changes. This change in direction is determined by the refractive index of each medium and the angle of incidence.
The law of refraction is given by Snell's law, which states:
n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
where n1 and n2 are the refractive indices of the initial and final mediums, respectively.
In this case, the initial medium is air and the final medium is glass, with a refractive index of 1.50. The angle of incidence is 45°.
Using Snell's law, we can calculate the angle of refraction as follows:
1.00 * sin(45°) = 1.50 * sin(angle of refraction)
sin(angle of refraction) = (1.00 * sin(45°)) / 1.50
sin(angle of refraction) = sin(45°) / 1.50
Using a scientific calculator or trigonometric table, we can find the value of sin(45°) ≈ 0.707106781
sin(angle of refraction) = 0.707106781 / 1.50
sin(angle of refraction) ≈ 0.4714
Now, to find the angle of refraction, we use the inverse sine function:
angle of refraction = arcsin(0.4714)
Using a calculator, we find that the angle of refraction is approximately 28.6°.
Therefore, the angle between the reflected and transmitted rays is the difference between the angle of reflection and the angle of refraction:
angle between reflected and transmitted rays = angle of reflection - angle of refraction
angle between reflected and transmitted rays = 45° - 28.6°
angle between reflected and transmitted rays ≈ 16.4°
So, the angle between the reflected and transmitted rays is approximately 16.4°.