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Reflection and Refraction of Light
257
22.50
Applying Snell’s law to this refraction gives
21
sin
sin
glass
air
nn
θ
=
If
1
2
2
=
, this becomes
( )
222
sin
sin 2
2sin
cos
ss
2
gla
n
θθ
==
or
2
cos
2
glass
n
=
Then, the angle of incidence is
11
12
1.56
2
2cos
2cos
22
glass
n
−−
=
77.5
= °
22.51
In the Figure at the right, observe that
1
90
β
=°
−
and
1
90
α
−
. Thus,
=
.
Similarly, on the right side of the
prism,
2
90
δ
−
and
2
90
γ
−
,
giving
=
.
Next, observe that the angle between
the reflected rays is
( ) ( )
B
βγ
+
+
=+
,
so
( )
2
B
+
=
. Finally, observe that the
left side of the prism is sloped at angle
from the vertical, and the right side is sloped at
angle
.
Thus, the angle between the two sides is
A
=
+
, and we obtain the result
()
=
BA
αγ
±
±
²
³
±
´
µ
²
³
²
³
±
³
±
³
²

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