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Reflection and Refraction of Light
261
22.57
Refer to the figure given at the right.
()
( )
12
43
min
δ
αε
θ
=+= − + −
abc
bcd
Note that triangles
and
are
congruent. Therefore,
β
γ
=
23
and their
complementary angles are also equal,
or
1
sin
n
=
.
From Snell’s law at point
a
,
2
sin
=
(1)
and at point
d
,
sin
sin
n
=
Since
=
, comparison of these results shows that
41
=
, so
( )
2
min
=−
.
But,
( )
2
90
90
90
2
A
θβ
=
°−
=
, or

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