Question $14$

$4$ pts

Light travels through a medium with an index of refraction $1\mathrm{.}401$ and is incident on a horizontal sheet of material with a different index of refraction. If the incident angle of the light is $40\mathrm{.}8$ degrees $($from the surface normal$)$ and the refracted ray in the sheet makes an angle of $54\mathrm{.}9$ degrees with the direction perpendicular to the surface of the sheet, what is the index of refraction for the sheet material?

Enter your answer as a decimal with no units. For example, if your calculations produce a value of $1\mathrm{.}23,$ enter your answer as $1\mathrm{.}23.$