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A beam of white light is incident on the surface of a diamond at an angle θa. (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 *n*_{r}_{ed} = 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:** Calculate* v*_{red}, the speed of red light in the diamond. To four significant figures c = 2.998 × 10^{8} m/s

**Part B:** Calculate* v*_{blue}, the speed of blue light in the diamond. To four significant figures c= 2.998 × 10^{8} m/s

** Part C:** Derive a formula for δ, the angle between the red and blue refracted rays in the diamond (Express the angle in terms of* n*_{red},* n*_{blue}, and *θa*. Use* n*_{air} = 1. Remember that the proper way to enter the inverse sine of* x* in this case is asin(x)

Revelant knowledge

Snell’s Law: A light beam contains an index reflection equal to the ratio n= c/v in which case we could calculate the angle of refraction by with the help of Snell’s Law: n_{1}sinθ_{1}=n_{2}sinθ_{2}

## 1 Answer