CHAPTER 36
IMAGE FORMATION
AND
OPTICAL
INSTRUMENTS
ActivPhysics
can help with these problems:
All activities in Section 15
Sections 361 and 362:
Plane and Curved
Mirrors
Problem
1.
A
shoe store uses small floorlevel [email protected] let
customers view prospective purchases. At what
angle should such a mirror be inclined so that a
person standing 50 cm from the mirror with eyes
140 cm off the floor can see her feet?
Solution
A small mirror (M) on the floor intercepts rays
coming from a customer's shoes (O), which are
traveling nearly parallel to the floor. The angle to the
customer's eye
(E) from the mirror is twice the angle
of reflection, so tan 2a
=
h/d,
or
a
=
tan'
x
(140150)
=
35.2", for the given distances. Therefore,
the plane of the mirror should be tilted by 35.2" from
the vertical to provide the customer with a floorlevel
view of her shoes.
Problem
1 Solution.
Problem
2. Two plane mirrors occupy the first four meters of
the positive
a and yaxes, as shown in Fig. 3644.
Find the locations of all images of an object at
z=2m,y=lm.
FIGURE
3644 Problem 2 Solution.
Solution
In addition
,to
the two direct images in each mirror
(one reflection)
at
I,
=
(2 m,
1 m) and
=
(2 m, 1 m),
a multiple image (two reflections) also
appears at
I,,
=
(2 m, 1 m). (The latter is the
image in one mirror of the direct image in the other.)
Ray tracing confirms this, as shown on Fig. 3644. No
more than two reflections are possible for
perpendicular mirror planes, so these are all the
images.
Problem
3. (a) What is the focal length of a concave mirror if
an object placed 50 cm in front of the mirror has a
real image 75 cm from the mirror? (b) Where and
what type will the image be if the object
is moved
to a point 20 cm from the mirror?
Solution
(a) The mirror equation relates the given distances
(both positive for a real object and image)
to the focal
length:
f'
=
(50 cm)I
+
(75 cm)l, or
f
=
30 cm.
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 Spring '10
 CatherineBordel
 Physics

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