In the figure below, where n_1 = 1.82, n_2 = 1.51, and n_3 = 1.35, light refract
ID: 1455101 • Letter: I
Question
In the figure below, where n_1 = 1.82, n_2 = 1.51, and n_3 = 1.35, light refracts from material 1 into material 2. If it is incident at point A at the critical angle for the interface between materials 2 and 3, what are (a) the angle of refraction at point B and (b) the initial angle 0? If, instead, light is incident at B at the critical angle for the interface between materials 2 and 3, what are (c) the angle of refraction at point A and (d) the initial angle 0? If, instead of all that, light is incident at points at Brewster's angle for the interface between materials 2 and 3, what are (e) the angle of refraction at point B and (f) the initial angle theta?Explanation / Answer
a)
angle of incidence at A = i = sin^-1(n3/n2) = 63.4
angle of incidence at B = 90-i = 26.6
from snells law
n2*sini = n3*sinr
1.51*sin26.6 = 1.35*sinr
r = 30 degrees <<----answer
(b)
n1*sintheta = n2*sini
1.81*sintheta = 1.51*sin63.4
theta = 47.9 <<<<--------answer
(c)
angle of incidence at B = i = sin^-1(n3/n2) = 63.4
angle of incidence at A = 90-i = 26.6
from snells law
n2*sini = n3*sinr
1.51*sin26.6 = 1.35*sinr
r = 30 degrees <<----answer
(d)
n1*sintheta = n2*sinr
1.81*sintheta = 1.51*sin30
theta = 24.5 <<<<--------answer
(e)
tanp = n3/n2
tanp = 1.35/1.51
p = 41.8
from snells law
n2*sinp = n3*sinr
1.51*sin41.8 = 1.35*sinr
r = 48.24 degrees <<<<--------answer
(f)
n1*sintheta = n2*sinp
1.82*sintheta = 1.51*sin41.8
theta = 33.6 <<<<--------answer
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