Refraction and Total Internal Reflection: A ray of light traveling in air strike

Question

Refraction and Total Internal Reflection: A ray of light traveling in air strikes a rectangular block of silicon nitride (whose index of refraction is: n=2.0) at an angle of 60 degree from the normal (at point "A"). The light enters the block and refracts towards point B, where it might refract back into the surrounding air, or it might suffer total internal reflection. a. Determine the angle of refraction at point A b. Determine the angle of incidence at point B c. Calculate the critical angle for light trying to cross the silicon nitride/air boundary d. Determine if at point B whether total internal reflection will occur or instead refraction back into the surrounding air.

Explanation / Answer

a) angle of refraction at point A is r

Using Snell's law

n1*sin(i) = n2*sin(r)

1*sin(60) = 2*sin(r)

sin(r) = sin(60)/2 = 0.433

r = sin^(-1)(0.433) = 25.65 deg

b) angle of incidence at B is i1 = 90-25.65 = 64.35 deg

C) critical angle is n = 1/sin(C)

sin(C) = 1/n = 1/2 = sin(30)

C = 30 degrees

D) Since angle of incidence at B is i1 = 64.35 > critical angle 30 deg ,hence total internal reflection takes place

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