Chapter 25
----------
Conceptual problem #1
The solution for this problem lies in the fact that if we
apply mirror reversal twice to the same letter of the sign, we will
get an un-reversed letter. A person in the store looking at the reversed
sign in a plane mirror will see the sign as not reversed,
Conceptual problem #3
Concave mirror is the choice since it will produces a real
image of the sun, i.e., it reflects all the light rays coming from
the sun and focuses them to one point. The sun is far away from
the mirror and all sun light rays are in practice parallel to each other
and the mirror can be aligned such that its pricipal axis is parallel to the
sun rays. The image of the sun will be in the focal point of the mirror.
Therefore, the paper to be ignited must be at a distance f from the mirror
(focal length).
1). Lets look at the figure and assign a letter O to a point where the two
mirrors touch each other. Follow the lines conneting the points indicated
to identify the angles discussed here.
The angle M2-M1-O between the outgoing ray and the first mirror is equal
to 90 - 65 = 25 degrees.
Since the sum of all the angles in the triangle is equal to 180 degrees,
the angle M1-M2-O is equal to 180 - 120 - 25 = 35 degrees,
The angle of reflection from the second mirror is a complementary one and
is equal to theta = 90 - 35 = 55 degrees.
5). The angle will be the same, 10 degrees. There are several ways of
arriving at this answer. The most laborious is to follow each reflection
and calculate all angles involved. A more elegant solution is based on
an observation that the mirror will produce a virtual image of the
source of the rays, which will leave this virual image with a divergence
of 10 degress and continue after transition from "behind the mirror" to
the path of the reflected rays.
16). Use the mirror equation,
1 1 1
--- + --- = --- =>
d0 d1 f
d1 = d0*f/(d0-f) = 17*38/(38-17) cm = 30.7cm