Snell's law:

$\overline{){{\mathbf{\eta}}}_{{\mathbf{1}}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{{\mathbf{\theta}}}_{{\mathbf{1}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{\eta}}}_{{\mathbf{2}}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{{\mathbf{\theta}}}_{{\mathbf{2}}}}$

θ_{1} is the angle of incidence and θ_{2} is the angle of refraction.

sinθ_{2} = (η_{1}/η_{2})sinθ_{1}

θ_{2} = sin^{−1} ((η_{1}/η_{2})sinθ_{1})

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 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.

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 θ_{a}. Use n_{air} = 1.

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