A light ray in air is incident on a water surface at a 44° angle of incidence. Find each of the following angles.
(b) the angle of refraction
°
To find the angle of refraction when a light ray travels from air to water, you can use Snell's Law. Snell's Law states that the ratio of the sines of the angle of incidence (θ1) to the angle of refraction (θ2) is equal to the ratio of the speeds of light in the two media:
n1*sin(θ1) = n2*sin(θ2)
where n1 and n2 are the indices of refraction for the two media, respectively.
For air (n1), the index of refraction is approximately 1.00, and for water (n2), the index of refraction is approximately 1.33.
Given that the angle of incidence (θ1) is 44°, we can find the angle of refraction (θ2) by rearranging Snell's Law:
sin(θ2) = (n1/n2)*sin(θ1)
Plugging in the values, we have:
sin(θ2) = (1.00/1.33)*sin(44°)
Calculating this expression, we find:
sin(θ2) ≈ (0.75)*sin(44°)
Using a scientific calculator, we can determine that:
sin(θ2) ≈ 0.604
To find the angle of refraction (θ2), take the inverse sine (sin^-1) of this value:
θ2 ≈ sin^-1(0.604)
Using a scientific calculator or reference table, we find:
θ2 ≈ 37.6°
Therefore, the angle of refraction is approximately 37.6°.