Question

The figure below shows the path of a beam of light through several layers with different indices of refraction. (n4 = 1.00)

(a) If θ1 = 31.0°, what is the angle θ2 of the emerging beam?
°

(b) What must the incident angle θ1 be in order to have total internal reflection at the surface between the medium with n = 1.20 and the medium with n4 = 1.00?

Answer 1

a .

for snell law ,

sin 31 / sin θ2 = n4 / 1 .6 = 1 / 1.6 ;   or θ2 = 55.49 degree

b .

since internal reflection occurs ,

θc in n = 1.2 ,    :   sin θc = 1 / 1.2 = 0.8333 ;

in n= 1.4 ,    sin i / sin θc = 1.2 / 1.4 ; or sin i = 0.8333 * ( 1 .2 / 1.4 ) = 0.714

in n = 1.6 ,   sin θ1 / sin i = 1.4 / 1.6 or sin θ1 = 0.714 * ( 1.4 / 1.6 ) = 0.625 ;

so incident angle , θ1 = 38.682 ;