Two light rays, one red and one violet, encounter a glass surface. If the index of refraction of the red light ray = 1.52, the index of refraction of the violet light ray = 1.54, and the angle of incidence = 30 degrees, calculate the angle of refraction of each colour of light ray (from air to glass).
- So considering that these light rays are travelling from air to glass, to find the angle of refraction of the red light ray, do I add its index of refraction and the index of refraction of air, or do I just use one of them (if so, which one)?
To find the angle of refraction of the red light ray, you need to use both the index of refraction of the red light ray and the index of refraction of air, in addition to the angle of incidence.
The index of refraction of a material describes how much the speed of light is reduced when traveling through that material compared to a vacuum or air. When light travels from one medium (such as air) to another (such as glass), it changes its speed and direction. This change is characterized by Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction between the two media.
In this case, the angle of incidence is given as 30 degrees, the index of refraction of the red light ray in glass is 1.52, and the index of refraction of air is approximately 1.00 (since the refractive index of air is very close to 1). To find the angle of refraction, you can use the formula:
sin(angle of incidence) / index of refraction of air = sin(angle of refraction) / index of refraction of red light in glass
Now, you can substitute the given values into the equation:
sin(30 degrees) / 1.00 = sin(angle of refraction) / 1.52
Simplifying the equation:
0.5 = sin(angle of refraction) / 1.52
To isolate the sin(angle of refraction), multiply both sides of the equation by 1.52:
1.52 * 0.5 = sin(angle of refraction)
0.76 = sin(angle of refraction)
To find the angle of refraction, take the inverse sine (or arcsine) of both sides of the equation:
angle of refraction = arcsin(0.76)
Using a calculator, you'll find that the angle of refraction for red light is approximately 50.543 degrees.
Repeat the same process to find the angle of refraction for the violet light ray, using the given index of refraction for violet light in glass (1.54) instead of the index of refraction for red light.
So, the angle of refraction for the violet light ray can be calculated as:
sin(30 degrees) / 1.00 = sin(angle of refraction) / 1.54
0.5 = sin(angle of refraction) / 1.54
1.54 * 0.5 = sin(angle of refraction)
0.77 = sin(angle of refraction)
angle of refraction = arcsin(0.77)
Using a calculator, you will find that the angle of refraction for violet light is approximately 51.709 degrees.