Final answer:
The window's index of refraction is approximately 1.5 (c) and is likely made of glass.
Step-by-step explanation:
The window's index of refraction can be determined using the equation: n = tan(θ), where θ is the angle of incidence. In this case, light is reflected at an angle of 55.6º and is completely polarized. To find the index of refraction, we need to find the tangent of 55.6º, which is approximately 1.53. Therefore, the window's index of refraction is closer to 1.5 (c).
The likely substance of which the window is made can be determined by comparing the calculated index of refraction to the known indices of various materials. For example, glass typically has an index of refraction ranging from 1.45 to 1.9. Since the window's index of refraction is closer to 1.5, it is likely that the window is made of glass.
When light reflected off a surface is completely polarized, this occurs at the Brewster's angle, which is directly related to the index of refraction of that surface. Brewster's law states that the tangent of the Brewster's angle equals the index of refraction. Since we know light is completely polarized at a 55.6° angle when reflected from the window, we can use the following equation:
tan(θ_b) = n_2/n_1
Given that n_1 (the index of refraction for air) is approximately 1.00, we can solve for n_2 (the index of refraction for the window material):
tan(55.6°) = n_2/1.00
Calculating the tangent of 55.6° gives us n_2, which is the index of refraction we are looking for.
n_2 = tan(55.6°) ≈ 1.43
The closest provided answer to 1.43 is c) 1.5, which often corresponds to crown glass or a similar type of glass.