wilson (kw22588) – HW12 – Mackie – (20224)
1
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14
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001
10.0 points
The reflecting surfaces of two intersecting flat
mirrors are at an angle of 56
◦
, as shown in
the figure. A light ray strikes the horizontal
mirror at an angle of 50
◦
with respect to the
mirror’s surface.
56
◦
50
◦
φ
Figure is not drawn to scale.
Calculate the angle
φ
.
Correct answer: 68
◦
.
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 (56
◦
)
=
68
◦
.
As a matter of interest,
in the upperhalf
of the figure the angles (clockwise) in the
triangles from left to right are
40
◦
,
40
◦
,
and 100
◦
;
80
◦
,
34
◦
,
and 66
◦
;
114
◦
,
16
◦
,
and 50
◦
;
130
◦
,
16
◦
,
and 34
◦
;
and in the lowerhalf of the figure the angles
(counterclockwise) in the triangles from left
to right are
16
◦
,
16
◦
,
and 148
◦
;
32
◦
,
34
◦
,
and 114
◦
;
66
◦
,
40
◦
,
and 74
◦
;
106
◦
,
40
◦
,
and 34
◦
.
002
10.0 points
An cylindrical opaque drinking glass has a
diameter 5
.
4 cm and height
h
, as shown in the
figure.
An observer’s eye is placed as shown
(the observer is just barely looking over the
rim of the glass). When empty, the observer
can just barely see the edge of the bottom
of the glass. When filled (with a transparent
liquid with an index of refraction of 1
.
26) to
the brim, the observer can just barely see the
center of the bottom of the glass.
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wilson (kw22588) – HW12 – Mackie – (20224)
2
θ
i
h
5
.
4 cm
θ
r
e
y
e
Calculate the angle
θ
r
.
Correct answer: 63
.
7321 degrees.
Explanation:
Looking at the figure below,
R
r
R
i
θ
i
h
r
d
θ
r
e
y
e
After filling the glass with liquid, we know
from Snell’s law that
n
liquid
sin
θ
i
=
n
air
sin
θ
r
.
The radius
r
is onehalf the diameter
d
, there
fore
sin
θ
i
≡
r
R
i
=
r
√
r
2
+
h
2
.
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 Spring '08
 Turner
 Physics, Snell's Law, Correct Answer, refractive index, Total internal reflection

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