A laser beam is incident on a 34°-56°-90° prism perpendicular to one of its faces, as shown in the figure below. The transmitted beam that exits the hypotenuse of the prism makes an angle of 15° with the direction of the incident beam. Find the index of refraction of the prism. (Use the following as necessary: θ1 = 15°, θ2 = 34°)