#1: If the angle of incidence is 30, what is the angle of refraction from air to water, air to glass, and glass to water?
#2: 45, angle from air to water, air to glass, and glass to water?
#3: 60, angle from air to water, air to glass, and glass to water?
#4: 90, angle from air to water, air to glass, and glass to water?
To answer these questions, we need to use Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two mediums.
1) If the angle of incidence is 30 degrees:
- Air to Water: Using Snell's Law, we have sin(30)/sin(angle of refraction in water) = velocity of light in air/velocity of light in water. The velocity of light in air is the same as in a vacuum and the velocity of light in water is 2/3 of the velocity in air. Therefore, sin(30)/sin(angle of refraction in water) = 1/(2/3) = 3/2. This implies that sin(angle of refraction in water) = 2/3 * sin(30) = 1/3. The angle of refraction in water is approximately 19.5 degrees.
- Air to Glass: The velocity of light in glass is usually around 2/3 of the velocity in air. So, sin(30)/sin(angle of refraction in glass) = 1/(2/3) = 3/2. This implies that sin(angle of refraction in glass) = 2/3 * sin(30) = 1/3. The angle of refraction in glass is also approximately 19.5 degrees.
- Glass to Water: Using Snell's Law, sin(angle of refraction in glass)/sin(angle of refraction in water) = velocity of light in glass/velocity of light in water. As we established earlier, the velocity of light in glass is 2/3 of the velocity in air, and the velocity of light in water is 2/3 of the velocity in air. Therefore, sin(angle of refraction in glass)/sin(angle of refraction in water) = (2/3)/(2/3) = 1. This implies that the angle of refraction in glass is equal to the angle of refraction in water, so it is also approximately 19.5 degrees.
2) If the angle of incidence is 45 degrees:
Using the same reasoning as above, we can determine the angles of refraction as follows:
- Air to Water: sin(angle of refraction in water) = 2/3 * sin(45) = 2/3 * √2 / 2 = √2/3. The angle of refraction in water is approximately 41.8 degrees.
- Air to Glass: sin(angle of refraction in glass) = 1/3 * sin(45) = 1/3 * √2 / 2 = √2/6. The angle of refraction in glass is approximately 24.3 degrees.
- Glass to Water: The angle of refraction in glass is equal to the angle of refraction in water, so it is still approximately 24.3 degrees.
3) If the angle of incidence is 60 degrees:
- Air to Water: sin(angle of refraction in water) = 2/3 * sin(60) = 2/3 * √3 / 2 = √3/3. The angle of refraction in water is approximately 35.3 degrees.
- Air to Glass: sin(angle of refraction in glass) = 1/3 * sin(60) = 1/3 * √3 / 2 = √3/6. The angle of refraction in glass is approximately 18.5 degrees.
- Glass to Water: The angle of refraction in glass is equal to the angle of refraction in water, so it is still approximately 18.5 degrees.
4) If the angle of incidence is 90 degrees (a ray of light is incident perpendicularly to the surface):
- Air to Water: Snell's Law cannot be applied in this case as the formula uses the sine of the angle of incidence. However, we know that the angle of refraction in water for a perpendicular incidence is 0 degrees.
- Air to Glass: Similarly, the angle of refraction in glass for a perpendicular incidence is also 0 degrees.
- Glass to Water: Since the angle of refraction in glass is 0 degrees, there is no angle of refraction in water as the light does not pass from glass into water.