A narrow ray of yellow light from glowing sodium (λ0 = 589 nm) traveling in air strikes a smooth surface of water at an angle of θi = 34.9°. Determine the angle of refraction θr.
To determine the angle of refraction (θr) for the narrow ray of yellow light passing from air to water, we can use Snell's law, which states that the ratio of the sines of the angles of incidence (θi) and refraction (θr) is equal to the ratio of the velocities of light in the two media:
n1 * sin(θi) = n2 * sin(θr)
where n1 is the refractive index of the medium of incidence (in this case, air) and n2 is the refractive index of the medium of refraction (in this case, water).
The refractive index of air (n1) is approximately equal to 1 since the difference in refractive index between air and vacuum is negligible.
The refractive index of water (n2) is approximately equal to 1.33.
Now we can substitute the values into Snell's law and solve for θr:
1 * sin(34.9°) = 1.33 * sin(θr)
First, we calculate sin(θr):
sin(θr) = (sin(34.9°))/1.33
θr ≈ arcsin((sin(34.9°))/1.33)
Using a calculator:
θr ≈ arcsin(0.4272)
θr ≈ 25.8°
Therefore, the angle of refraction (θr) for the yellow light passing from air to water is approximately 25.8°.
To determine the angle of refraction (θr), we can use Snell's Law, which states:
n1 * sin(θi) = n2 * sin(θr)
where:
- n1 is the refractive index of the initial medium (air)
- θi is the angle of incidence
- n2 is the refractive index of the second medium (water)
- θr is the angle of refraction
The refractive index of air (n1) is approximately 1.0003, and the refractive index of water (n2) is approximately 1.333.
Substituting the given values into Snell's Law:
1.0003 * sin(34.9°) = 1.333 * sin(θr)
To solve for θr, rearrange the equation:
sin(θr) = (1.0003 * sin(34.9°))/1.333
Using a scientific calculator, evaluate the right side of the equation:
sin(θr) ≈ 0.4978
To find the angle θr, take the inverse sine (sin^(-1)) of 0.4978:
θr ≈ sin^(-1)(0.4978)
Calculating this value using a scientific calculator, θr ≈ 30.2°
Therefore, the angle of refraction θr is approximately 30.2°.
the refractive index (n) for water is ... 4/3
... it is 1 for air
(n air) * sin(Θi) = (n water) * sin(Θr) ... this is Snell's law