**A Sparkling Diamond I**

Part A = 1.244*10^8 m/s

Part B = 1.224*10^8 m/s

Part C = δ = asin(sin(theta;_{a}) / n_{red}) – asin(sin(theta;_{a}) / n_{blue})

Part D = δ = 0.287°

**Solution Below:**

_{a}. 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 n

_{red}= 2.410 for red light and n

_{blue}= 2.450 for blue light. The surrounding air has n

_{air}= 1.000. Note that the angles in the figure are not to scale.

Part A

_{red}, the speed of red light in the diamond. To four significant figures, c = 2.998 * 10^8m/s.

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

The speed of light in a medium is:

c = (2.998 * 10^8) * (1.00 / n_{medium})

For red light in diamond:

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

c = 1.244*10^8 m/s

1.244*10^8 m/s

Part B

_{red}, the speed of blue light in the diamond. To four significant figures, c = 2.998 * 10^8m/s.

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

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

1.224*10^8 m/s

Part C

Start with Snell’s law:

n_{air} * sin(θ_{1}) = n_{diamond} * sin(θ_{2})

For red light, the above becomes:

sin(θ_{1}) = n_{red} * sin(θ_{2, red})

θ_{2, red} = asin(sin(θ_{1}) / n_{red})

And for blue light:

sin(θ_{1}) = n_{blue} * sin(θ_{2, blue})

θ_{2, blue} = asin(sin(θ_{1}) / n_{blue})

Since we want the difference between the angles:

δ = asin(sin(θ_{1}) / n_{red}) – asin(sin(θ_{1}) / n_{blue})

δ = asin(sin(θ_{1}) / n_{red}) – asin(sin(θ_{1}) / n_{blue})

Part C

_{a}= 45°.

Just use the formula from Part D:

δ = asin(sin(θ_{1}) / n_{red}) – asin(sin(θ_{1}) / n_{blue})

δ = asin(sin(45°) / 2.410) – asin(sin(45°) / 2.450)

δ = 16.7751° – 17.0619

δ = 0.2868°

round:

0.287°

Typo on Part D,

δ = asin(sin(45°) / 2.450) – asin(sin(45°) / 2.450)

= 0

should be:

δ = asin(sin(45°) / 2.410) – asin(sin(45°) / 2.450)

correct answer though

Thanks, should be fixed now!

The answer to Part B is incorrect. It should be 1.224*10^8

Good catch, sorry about that one. Sometimes the typos slip through