A ray of light in a tank of water has an angle of incidence of 23°. What is the angle of refraction in air? (Enter 0 if total internal reflection occurs.)
To find the angle of refraction in air, 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 speeds of light in the two media.
Snell's Law can be written as:
n1 * sin(θ1) = n2 * sin(θ2)
Where:
- n1 is the refractive index of the initial medium (water)
- n2 is the refractive index of the second medium (air)
- θ1 is the angle of incidence
- θ2 is the angle of refraction
The refractive index of water is approximately 1.33, and the refractive index of air is about 1.00.
Let's calculate the angle of refraction:
n1 * sin(θ1) = n2 * sin(θ2)
1.33 * sin(23°) = 1.00 * sin(θ2)
Now, we can solve for θ2:
sin(θ2) = (1.33 / 1.00) * sin(23°)
sin(θ2) = 1.33 * sin(23°)
sin(θ2) ≈ 0.4983
To find the angle θ2, we can use the arcsin function (also known as sin^-1) on a calculator:
θ2 = arcsin(0.4983)
θ2 ≈ 29° (rounded to the nearest degree)
Therefore, the angle of refraction in air is approximately 29°.