The index of refraction for crown glass is 1.512 at a wavelength of 660 nm (red), whereas its index of refraction is 1.530 at a wavelength of 410 nm (violet). If both wavelengths are incident on a slab of crown glass at the same angle of incidence, 1.1°, what is the angle of refraction for each wavelength?

red °
violet

To calculate the angles of refraction for each wavelength, we can 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 indices of refraction of the two media:

n1 * sin(θ1) = n2 * sin(θ2)

Where:
n1 = index of refraction of the initial medium (air or vacuum)
θ1 = angle of incidence
n2 = index of refraction of the second medium (crown glass)
θ2 = angle of refraction

We are given the following information:
- For red light (wavelength = 660 nm), the index of refraction of crown glass is 1.512.
- For violet light (wavelength = 410 nm), the index of refraction of crown glass is 1.530.
- The angle of incidence for both wavelengths is 1.1°.

Let's calculate the angle of refraction for red light first (wavelength = 660 nm):

n1 * sin(θ1) = n2 * sin(θ2)

Since the angle of incidence (θ1) is given as 1.1°, we need to convert it to radians:

θ1 = 1.1° * π/180 ≈ 0.0191 radians

Now we can substitute the values into Snell's Law:

1 * sin(0.0191) = 1.512 * sin(θ2)

sin(θ2) = (1 * sin(0.0191)) / 1.512
sin(θ2) ≈ 0.0126

To find the angle of refraction (θ2), we can take the inverse sine of 0.0126:

θ2 ≈ arcsin(0.0126) ≈ 0.721°

Therefore, the angle of refraction for red light is approximately 0.721°.

Now let's calculate the angle of refraction for violet light (wavelength = 410 nm):

Using the same approach, we have:

n1 * sin(θ1) = n2 * sin(θ2)

θ1 = 1.1° * π/180 ≈ 0.0191 radians

sin(θ2) = (1 * sin(0.0191)) / 1.530
sin(θ2) ≈ 0.0125

θ2 ≈ arcsin(0.0125) ≈ 0.714°

Therefore, the angle of refraction for violet light is approximately 0.714°.

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