Question

A narrow beam of sodium yellow light, with wavelength 589 nm in vacuum, is incident from air onto a smooth water surface at an angle of incidence of 40 degrees with respect to the normal. The index of refraction of water is 1.33. What is the angle of refraction in degrees

Answer 1

Using Snell's Law, the angle of refraction for a narrow beam of sodium yellow light with a wavelength of 589 nm going from air to water with an angle of incidence of 40 degrees is approximately 28.7 degrees.

Step-by-step explanation:

To find the angle of refraction when a narrow beam of sodium yellow light, with a wavelength of 589 nm in vacuum, is incident from air onto a smooth water surface, we use Snell's Law. Snell's Law states that n1 * sin(i) = n2 * sin(r), where n1 is the refractive index of the first medium (air in this case, with an index of 1.0), i is the angle of incidence, n2 is the refractive index of the second medium (water, with an index of 1.33), and r is the angle of refraction. Given an angle of incidence of 40 degrees, we can solve for r.

n1 * sin(i) = n2 * sin(r)

1.0 * sin(40 degrees) = 1.33 * sin(r)

sin(r) = sin(40 degrees) / 1.33

sin(r) ≈ 0.643 ≈ 0.484

r ≈ sin-1(0.484)

r ≈ 28.7 degrees

Answer 2

28.9°

Step-by-step explanation:

Parameters given:

Angle of incidence, i = 40°

Refractive index, n = 1.33

Refractive index is the ratio of the sine of the angle of incidence, i, and the sine of the angle of refraction, r :

`n =(sin(i))/(sin(r))`

Therefore:

=>
`1.33 = (sin40)/(sin(r)) \\\\\\sin(r) = (0.6428)/(1.33)\\ \\\\sin(r) = 0.4833\\\\\\r = sin^(-1)(0.4833)`

r = 28.9°

The angle of refraction is 28.9°.