Snell's law:

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

i = 90 - 30 - ϕ_{1} = 90 - 30 - 41.3 = 18.7°

From triangle ABC:

Red light is incident in air on a 30- 60- 90(degree) prism as shown. The incident beam is directed at an angle of ϕ_{1} = 41.3° and ϕ_{2} = 46.64° with respect to the horizontal and enters the prism at a height h = 17 cm above the base. The beam leaves the prism to the air at a distance d = 45.5 along the base as shown.

What is n, the index of refraction of the prism for red light?

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