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A laser beam is incident on a $45^{\circ}-45^{\circ}-90^{\circ}$ prism perpendicular to one of its faces, as shown in Figure P 22.20 . The transmitted beam that exits the hypotenuse of the prism makes an angle of $\theta=15.0^{\circ}$ with the direction of the incident beam. Find the index of refraction of the prism.

$1.22$

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so, looking at the figure, a light rays incident perpendicular to one of the faces of the prism. The light transmitted through the prism and leaves the hype oddness face with the refraction angle of 15 degrees has shown in the figure. Thus, three fraction of light takes place on Lee at the iPod. News face from the figure. The angle of incident at the high pot news face of the triangle is 45 degrees and the angle of refraction would then be 45 plus 15 degrees. So we're gonna call this angle of refraction. They are equal to 45 degrees plus 15 degrees, which comes out to equal. Make that look more like degrees here, 60 degrees. And then using Snell's law, we can find the, uh, index every fraction of the medium. So the index of refraction of the medium is from the incident side. So an eye is equal to the sign of the incident angle. They die. And this is equal to the index every fraction of the refracted medium. In our times, the sign of refraction signed data are we just found. Okay, so then the index of refraction of the incident medium medium is going to be equal to the index of refraction of the medium, which it travels into, which is air. So that's gonna be 1.0 times the ratio of signed data are, which was 60 degrees. Oh, divided by sign of the incident angle, which from the figure we can see is 45 degrees. Plugging those values in this expression, we find that this is equal to 1.22 which weakened boxing as our solution to the question.