Optics: Snells law and refraction question. Imagine a prism with a cross section

Question

Optics: Snells law and refraction question.

Imagine a prism with a cross section that appears as a triangle with two 45 degree angles and a right angle. If a beam of light strikes the face opposite one of the 45 degree angles at normal incidence and then reflects of the face opposite the 90 degree face due to critical internal reflection and then leaves through the face opposite the other 45 degree angle, what is index of refraction of the prism material?

I'll certainly upvote the best answer, thanks so much in advanced for the help.

Explanation / Answer

Let the index of refraction of the prism material = n1
µ(air) = 1
and i = 45
At critical angle (i) , angle of refraction (r) = 90

According to Snell's Law :-
n1 * sin i = 1 * sin(90)
n1 = 1/sin(45)
n1 = 1.41
Index of refraction of the prism material, n1 = 1.41

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