In the figure shown, the equilateral prism is surrounded by air, and the light b

Question

In the figure shown, the equilateral prism is surrounded by air, and the light beam strikes surface 2 at the critical angle. Find the angle of incidence at surface 1, if the index of refraction for the glass prism is 1.45.

a) 27.9 degrees

b) 31.7 degrees

c) 35.6 degrees

d) 21.0degrees

e) 4.2 degrees

In the figure shown, the equilateral prism is surrounded by air, and the light beam strikes surface 2 at the critical angle. Find the angle of incidence at surface 1, if the index of refraction for the glass prism is 1.45. a) 27.9 degrees b) 31.7 degrees c) 35.6 degrees d) 21.0degrees e) 4.2 degrees

Explanation / Answer

The critical angle is

Acrit = Arcsin(1/n)

Acrit = 43.6 degrees

Thus, the refracted angle at the first interface is, by some geometry,

Ar = 16.4 degrees

Note that from Snell's law,          
          
n1sin(t1) = n2sin(t2)          
          
where          
          
n1 = index of refraction of first medium =    1.45
t1 = angle of incidence = 16.4   degrees  
n2 = index of refraction of second medium =    1  
t2 = angle of refraction = degrees  
          
Thus,          
          
t2 =    24.17   degrees   [ANSWER]

I wonder why this is not one of the choices. Is there a typo in your choices? I checked it three times.

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