Physics - Optics

An incident beam strikes a prism with a small angle of 20 degrees (the light enters perpendicular to the prism but the other side of the prism is slanted 20 degrees). The microwave signal is maximized when the receiver makes an angle of θ = 7 degrees relative to the incident direction.
(a) What is the angle of incidence (in degrees) when the beam exits the prism θi?
(b) What is the angle of refraction θr ?
(c) The index of refraction of the air surrounding the prism is 1.00. What is the index of refraction of the prism?
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I have no idea how to approach the problem. I know Snell's Law says that
n1sin(theta1) = n2sin(theta2), but I don't know the n for the prism, and I don't know why it's asking for the angle of incidence if it says it came in at 90 degrees to the prism.

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  1. I think I have made some progress:
    (a) The angle of incidence must also be 20 degrees
    (b) The angle of refraction must be 27 degrees
    (c) The index of refraction for the prism must be:
    Nprism*sin(20) = 1*sin(27), then:
    Nprism = sin(27)/sin(20) = 1.33

    Is this correct?

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