Golshani (ag5873) – Homework 01 – Yao – (57045)
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001
10.0 points
The reflecting surfaces of two intersecting flat
mirrors are at an angle of 62
◦
, as shown in
the figure. A light ray strikes the horizontal
mirror at an angle of 49
◦
with respect to the
mirror’s surface.
62
◦
49
◦
φ
Figure is not drawn to scale.
Calculate the angle
φ
.
Correct answer: 56
◦
.
Explanation:
Basic Concept:
θ
incident
=
θ
reflected
Solution:
θ
1
θ
2
φ
θ
Figure is to scale.
The sum of the angles in a triangle is 180
◦
.
In the triangle on the left we have angles
θ ,
180
◦

θ
1
2
,
and
180
◦

θ
2
2
,
so
180
◦
=
θ
+
180
◦

θ
1
2
+
180
◦

θ
2
2
,
or
θ
1
+
θ
2
= 2
θ .
(1)
In the triangle on the right we have angles
θ
1
,
θ
2
,
and
φ .
180
◦
=
θ
1
+
θ
2
+
φ ,
so
θ
1
+
θ
2
= 180
◦

φ .
(2)
Combining Eq. 1 and 2, we have
φ
= 180
◦

2
θ
= 180
◦

2 (62
◦
)
=
56
◦
.
As a matter of interest,
in the upperhalf
of the figure the angles (clockwise) in the
triangles from left to right are
41
◦
,
41
◦
,
and 98
◦
;
82
◦
,
28
◦
,
and 70
◦
;
110
◦
,
21
◦
,
and 49
◦
;
131
◦
,
21
◦
,
and 28
◦
;
and in the lowerhalf of the figure the angles
(counterclockwise) in the triangles from left
to right are
21
◦
,
21
◦
,
and 138
◦
;
42
◦
,
28
◦
,
and 110
◦
;
70
◦
,
41
◦
,
and 69
◦
;
111
◦
,
41
◦
,
and 28
◦
.
002
10.0 points
Consider a light ray which enters from air to
a liquid, where the index of refraction of the
liquid is given by
n
=
√
2.
n
= 1
n
=
√
2
Air
Liquid
light
ray
Denote the wavelength and the frequency
in the liquid by
λ
′
and
f
′
and those in the air
by
λ
and
f
. Choose the correct pair of ratios:
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Golshani (ag5873) – Homework 01 – Yao – (57045)
2
1.
λ
′
λ
= 2
,
f
′
f
= 1
2.
λ
′
λ
=
1
√
2
,
f
′
f
=
√
2
3.
λ
′
λ
=
1
2
,
f
′
f
= 1
4.
λ
′
λ
=
1
2
,
f
′
f
=
√
2
5.
λ
′
λ
=
√
2
,
f
′
f
=
√
2
6.
λ
′
λ
= 1
,
f
′
f
=
√
2
7.
λ
′
λ
=
√
2
,
f
′
f
= 1
8.
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 Fall '10
 YAO
 Snell's Law, Correct Answer, Total internal reflection, Geometrical optics

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