A narrow ray of yellow light from glowing
sodium (λ 0 = 589 nm) traveling in air strikes
a smooth surface of water at an angle θi =
16.5◦
.
Find the angle of refraction, θr.
Answer in units of ◦
To find the angle of refraction, θr, you can use Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two media involved. Snell's Law is expressed as:
n1 * sin(θi) = n2 * sin(θr)
Where:
n1 is the index of refraction of the incident medium (in this case, air),
n2 is the index of refraction of the refracted medium (in this case, water),
θi is the angle of incidence,
θr is the angle of refraction.
Given that the angle of incidence, θi = 16.5°, and the incident medium is air, which has an index of refraction approximately equal to 1, we can rewrite the equation as:
1 * sin(16.5°) = n2 * sin(θr)
Now, we need to find the index of refraction for water. The index of refraction of water varies with the wavelength of light, but for visible light, it is approximately equal to 1.33.
Plugging in the values, we have:
1 * sin(16.5°) = 1.33 * sin(θr)
To solve for θr, rearrange the equation:
sin(θr) = (1 * sin(16.5°)) / 1.33
Now, take the inverse sine (sin^(-1)) of both sides to find θr:
θr = sin^(-1)((1 * sin(16.5°)) / 1.33)
Using a scientific calculator, compute the expression to find θr. The result will be the angle of refraction, θr, in units of degrees.