A thick sheet of plastic, n = 1.500, is used as the side of an aquarium tank. Light reflected from a fish in the water has an angle of incidence of 30.0°. At what angle does the light enter the air?
To find the angle at which the light enters the air, we need to use Snell's Law, which relates the angles and indices of refraction for light passing from one medium to another.
Snell's Law is expressed as:
n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
In this case, the initial medium is water, where the refractive index is n1 = 1.500, and the final medium is air, where the refractive index is n2 = 1.000 (since the refractive index of air is very close to 1).
The angle of incidence is given to be 30.0°.
Rearranging Snell's Law to solve for the angle of refraction, we get:
angle of refraction = arcsin((n1 * sin(angle of incidence)) / n2)
Substituting the given values:
angle of refraction = arcsin((1.500 * sin(30.0°)) / 1.000)
Now, we can calculate the angle of refraction using a scientific calculator or an online trigonometric calculator.
After evaluating the expression, we find that the angle of refraction is approximately 49.0°.
Therefore, the light enters the air at an angle of approximately 49.0°.