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Reflection and Refraction of Light
255
(b)
Repeating the steps of part (a) with the index of refraction of air replaced by that of
water yields
3
63.5
θ
≥°
,
2
26.5
≤°
,
1
sin
0.499
≤
, and
1
30.0
.
(c)
Total internal reflection is
not possible since
polystyrene
carbon disulfide
nn
<
22.47
Applying Snell’s law at points A, B, and C, gives
1
1.40sin
1.60sin
αθ
=
(1)
1.20sin
1.40sin
β
α
=
(2)
and
2
1.00sin
1.20sin
=
(3)
Combining equations (1), (2), and (3) yields
21
sin
1.60sin
θθ
=
(4)
Note that equation (4) is exactly what Snell’s law would yield if the second and third
layers of this “sandwich” were ignored. This will always be true if the surfaces of all the
layers are parallel to each other.
(a) If
1
30.0
=°
, then equation (4) gives
()
1
2
sin
1.60sin30.0
53.1
−
=
°
(b)
At the critical angle of incidence on the lowest surface,

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