Create assignment, 00224, Homework 9, Apr 08 at 6:09 pm
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Hinged Mirrors 01
35:04, highSchool, numeric,
>
1 min, wording
variable.
001
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 53
◦
with respect to the
mirror’s surface.
56
◦
53
◦
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
37
◦
,
37
◦
,
and 106
◦
;
74
◦
,
34
◦
,
and 72
◦
;
108
◦
,
19
◦
,
and 53
◦
;
127
◦
,
19
◦
,
and 34
◦
;
and in the lowerhalf of the figure the angles
(counterclockwise) in the triangles from left
to right are
19
◦
,
19
◦
,
and 142
◦
;
38
◦
,
34
◦
,
and 108
◦
;
72
◦
,
37
◦
,
and 71
◦
;
109
◦
,
37
◦
,
and 34
◦
.
keywords:
Perpendicular Mirrors
35:04, trigonometry, numeric,
>
1 min, nor
mal.
002
Consider the case in which light ray A is in
cident on
mirror 1
, as shown in the figure.
The reflected ray is incident on
mirror 2
and
subsequently reflected as ray B. Let the an
gle of incidence (with respect to the normal)
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Create assignment, 00224, Homework 9, Apr 08 at 6:09 pm
2
on
mirror 1
be
θ
A
= 53
◦
and the point of
incidence be located 20 cm from the edge of
contact between the two mirrors.
90
◦
x
A
B
mirror 1
mirror 2
θ
A
θ
B
What is the angle of the reflection of ray B
(with respect to the normal) on
mirror 2
?
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 Spring '10
 Avram
 Physics, Work, Angle of Incidence, Snell's Law, Total internal reflection, ray B

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