Question

 A beam of white light is incident on the surface of a diamond at an angle θ_a.(Figure 1) Since the index of refraction depends on the light's wavelength, the different colors that comprise white light will spread out as they pass through the diamond. The indices of refraction in diamond are Tred = 2.410 for red light and Mblue = 2.450 for blue light. The surrounding air has Tair = 1.000. Note that the angles in the figure are not to scale.

 Part A

 Calculate Ured, the speed of red light in the diamond. To four significant figures, c = 2.998 x 10⁸ m/s.

 Part B

 Calculate ublue, the speed of blue light in the diamond. To four significant figures, c = 2.998 x 10⁸ m/s.

 Part C

 Derive a formula for S, the angle between the red and blue refracted rays in the diamond.

Answer 1

a)  c = 2.998 * 10^8m/s.

The speed of light in a medium is:

c = (2.998 * 10^8) * (1.00 / nmedium)

For red light in diamond:

c = (2.998 * 10^8) * (1.00 / 2.410)
c = 1.244*10^8 m/s

b)

Just solve like in Part A. For blue light in diamond, n = 2.450.

c = (2.998 * 10^8) * (1.00 / 2.450)
c = 1.224*10^8 m/s

c)

Start with Snell’s law:

nair * sin(θ1) = ndiamond * sin(θ2)

For red light, the above becomes:

sin(θ1) = nred * sin(θ2, red)
θ2, red = asin(sin(θ1) / nred)

And for blue light:

sin(θ1) = nblue * sin(θ2, blue)
θ2, blue = asin(sin(θ1) / nblue)

Since we want the difference between the angles:

δ = asin(sin(θ1) / nred) – asin(sin(θ1) / nblue)

δ = asin(sin(θ1) / nred) – asin(sin(θ1) / nblue)

Calculate δ numerically for θa = 45°.

Just use the formula

δ = asin(sin(θ1) / nred) – asin(sin(θ1) / nblue)
δ = asin(sin(45°) / 2.410) – asin(sin(45°) / 2.450)
δ = 16.7751° – 17.0619
δ = 0.2868°