a ray of light is incident on an air-glass boundary at 30 degrees. The index of refraction of air is 1,and the index of refraction for the glass is 1.4. What is the angle of the reflected ray, and what is the angle of the refracted ray?
Thanks in advance. Been stuck for three days.
To determine the angle of the reflected and refracted rays, you can apply the laws of reflection and refraction. The laws are as follows:
1. Law of Reflection: The angle of incidence is equal to the angle of reflection.
2. Snell's Law: The ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media.
Given:
Angle of incidence (θi) = 30°
Index of refraction of air (n1) = 1
Index of refraction of glass (n2) = 1.4
Now, let's calculate the angle of the reflected ray (θr) using the law of reflection:
Angle of incidence (θi) = Angle of reflection (θr)
θr = θi
θr = 30°
According to Snell's Law, the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media:
sin(θi) / sin(θr) = n2 / n1
sin(30°) / sin(θr) = 1.4 / 1
(1/2) / sin(θr) = 1.4
sin(θr) = 1 / (1.4 * 2)
sin(θr) = 0.357
To find the angle of the refracted ray, we can calculate the inverse sine of this value:
θr = arcsin(0.357)
θr ≈ 21.35°
Therefore, the angle of the reflected ray (θr) is 30°, and the angle of the refracted ray (θr) is approximately 21.35°.