The Law of Reflection
Light is known to behave in a very predictable manner. If a
ray of light could be observed approaching and reflecting off of a flat mirror,
then the behavior of the light as it reflects would follow a predictable lawknown as the law of reflection. The diagram below
illustrates the law of reflection.
In the diagram, the ray of light approaching the mirror is
known as the incident ray (labeled I in the diagram). The ray of
light that leaves the mirror is known as the reflected ray (labeled R in the diagram). At the
point of incidence where the ray strikes the mirror, a line can be drawn
perpendicular to the surface of the mirror. This line is known as a normal line (labeled N in the diagram). The normal line divides the angle between the incident ray and the reflected
ray into two equal angles. The angle between the incident ray and the normal is
known as the angle of incidence. The angle between the
reflected ray and the normal is known as the angle of reflection. (These two angles are labeled with
the Greek letter "theta" accompanied by a subscript; read as
"theta-i" for angle of incidence and "theta-r" for angle of
reflection.) The law of reflection states that when a ray of light reflects off
a surface, the angle of incidence is equal to the angle of reflection.
Reflection
and the Locating of Images
It is common to observe this law at work in a Physics lab
such as the one described in the previous part of Lesson 1. To view an
image of a pencil in a mirror, you must sight along a line at the image
location. As you sight at the image, light travels to your eye along the path
shown in the diagram below. The diagram shows that the light reflects off the
mirror in such a manner that the angle of incidence is equal to the angle of
reflection.
It just so happens that the light that travels along the line
of sight to your eye follows the law of reflection. (The reason for this will
be discussed later in Lesson 2). If you were to sight along a line at a
different location than the image location, it would be impossible for a ray of
light to come from the object, reflect off the mirror according to the law of
reflection, and subsequently travel to your eye. Only when you sight at the
image, does light from the object reflect off the mirror in accordance with the
law of reflection and travel to your eye. This truth is depicted in the diagram
below.
For example, in Diagram A above,
the eye is sighting along a line at a position above the actual image location. For light
from the object to reflect off the mirror and travel to the eye, the light
would have to reflect in such a way that the angle of incidence is less than
the angle of reflection. In Diagram B above, the eye is sighting along a line
at a position below the actual image location. In this
case, for light from the object to reflect off the mirror and travel to the
eye, the light would have to reflect in such a way that the angle of incidence
is more than the angle of reflection. Neither of these cases would follow the
law of reflection. In fact, in each case, the image is not seen when sighting
along the indicated line of sight. It is because of the law of reflection that
an eye must sight at the image location in order to see the image of an object
in a mirror.
Check Your Understanding
1. Consider the diagram at the right. Which one of the angles (A, B, C,
or D) is the angle of incidence? ______ Which one
of the angles is the angle of reflection? ______
Angle B is the
angle of incidence (angle between the incident ray and the normal). Angle C is
the angle of reflection (angle between the reflected ray and the normal).
2. A ray of light is incident towards a plane mirror at an
angle of 30-degrees with the mirror surface. What will be the angle of
reflection?
The angle of
reflection is 60 degrees. (Note that the angle of incidence is not 30 degrees;
it is 60 degrees since the angle of incidence is measured between the incident
ray and the normal.)
close
3. Perhaps you have observed the image of the sun in the
windows of distant buildings near the time that the sun is rising or setting.
However, the image of the sun is not seen in the windows of distant building
during midday. Use the diagram below to explain, drawing appropriate light rays
on the diagram.
A ray of light
drawn from the sun's position at 7 pm to the distant window reflects off the
window and travel to the observer's eye. On the other hand, a ray of light
drawn from the 1 pm sun position to the window will reflect and travel to the
ground, never making it to the distant observer's eye.
4. A ray of light is approaching a set of three mirrors as
shown in the diagram. The light ray is approaching the first mirror at an angle
of 45-degrees with the mirror surface. Trace the path of the light ray as it
bounces off the mirror. Continue tracing the ray until it finally exits from
the mirror system. How many times will the ray reflect before it finally exits?
The light
reflects twice before it finally exits the system. Draw a normal at the point
of incidence to the first mirror; measure the angle of incidence (45 degrees);
then draw a reflected ray at 45 degrees from the normal. Repeat the process for
the second mirror.