Question

A beam of white light is incident on the surface of a diamond at an angle ?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 nred=2.410 for red light and nblue=2.450 for blue light. The surrounding air has nair=1.000. Note that the angles in the figure are not to scale.

Part A

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

Express your answer in meters per second to four significant digits.

Part B

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

Express your answer in meters per second to four significant digit

Part C

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

Express the angle in terms of nred, nblue, and ?a. Use nair=1. Remember that the proper way to enter the inverse sine of x in this case is asin(x)

Answer 1

A) Vair* nair = Vred * nred

2.998×10^8 * 1 = Vred * 2.41

Vred = 1.244 * 10^8 m/s

B)

Vair* nair = Vblue * nblue

2.998×10^8 * 1 = Vblue * 2.45

Vblue = 1.223 * 10^8 m/s

C) Using Snells law

na*sin(θa) = nred*sin(θred)

sin(θred) = (na/nred)*sin(θa)

θred = asin[(na/nred)*sin(θa)]

Similarly,

sin(θblue) = (na/nblue)*sin(θa)

θblue = asin[(na/nblue)*sin(θa)]

Therefore, the angle between the red and blue refracted rays in the diamond = δ = θred - θblue

δ = asin[(na/nred)*sin(θa)] - asin[(na/nblue)*sin(θa)]