CHAPTER 25 THE REFLECTION OF LIGHT
We use mirrors to reflect light and form images. To
help us understand how these images are formed, we
must understand wave fronts and rays.
A wave front is a surface on a traveling wave where the
phase is everywhere the same.
In the case of sound, a wave front would be drawn
through a spherical shell where the compression is a
maximum. This series of concentric shells would be a
series of wave fronts. The direction of travel of these
wave fronts would be represented by rays.
Light produces wave fronts in the same manner with
variations in electric and magnetic field strength
replacing compressions and rarefactions.
Light waves generally spread out in a spherical fashion
from a source. so the wave front is curved. If the source
is far enough away from the wave front being studied,
the wave front can be considered to be a plane wave
front.
The rays are always perpendicular to the wave front. In
the case of a plane wave front, the rays are parallel.
When light is incident on a surface it can be absorbed,
scattered, refracted, transmitted, undergo diffuse
reflection or regular reflection. In this chapter we will
be studying regular reflection.
Any time light is reflected, it obeys the Law of
Reflection which states: The incident ray, the reflected
ray, and the normal to the surface all lie in the same
plane and the angle of reflection equals the angle of
incidence.
Regular or specular reflection occurs with mirrors and
other shiny surfaces. Diffuse reflection occurs with
rough surfaces such as flat paint, most clothing, etc.
Formation of Images by a Plane Mirror.
In the lab we investigated this type of image formation,
first for a point and then for a triangle. These are the
characteristics of the image formed by a plane mirror.
1. The image is upright.
2. The image is the same size as the object.
3. The image distance is the same as the object distance.
4. The image is virtual.
5. The image is reversed, right to left.
The formation of an image in a plane mirror is
illustrated above. Notice that no light actually comes
from the location of the image to the eye. That is what
defines this image as virtual.
This illustration shows how we know the object distance
is equal to the image distance in the case of a plane
mirror. Notice that the two triangles are congruent.
Sometimes this branch of optics is called geometrical
optics for obvious reasons.
Mirrors and lenses
Spherical Mirrors
A spherical mirror has a curved surface that reflects
light in a regular fashion. Its curvature is determined by
the size of the sphere it could have been cut from. The
radius of the sphere is equal to the radius of curvature
of the mirror.
On the left we see a concave mirror since the light
strikes the inside surface of the original sphere. On the
right we have a convex mirror since the light strikes the
outside of the original sphere. If the center of the mirror
curves toward the light source, the mirror is convex. If
the center of the mirror curves away from the light
source, it is concave.
Of the three types of mirrors, only concave mirrors can
form a real image.
This real image is formed since light rays from the
object actually converge at some point in front of the
mirror. If we place a screen there, we will see the image
of the object on the screen. We will see that it is also
possible to place the object at a location relative to the
mirror where a real image will not form. This type of
mirror is called a converging mirror.
In the case of a convex mirror, as with a plane mirror,
only a virtual image can be formed.
As you can see, rays from a single point will always
diverge after striking the surface forming a virtual
image. This type of mirror is called a diverging mirror.
In both cases, the focal length F is the distance relative
to the vertex of the mirror where an image is formed
from incoming parallel rays. In the case of the concave
mirror, it is positive> In the case of the convex mirror,
it is negative.
In both cases the magnitude of the focal length is equal
to one half the radius of curvature.
Spherical aberration is a distortion of an image formed
by spherical mirrors due to the fact that parallel
incoming rays farthest from the principal axis are not
reflected through the focal point.
This is corrected by using mirrors with a parabolic
surface so that all the parallel incoming rays pass
through the focal point.
Formation of Images by Spherical Mirrors
Ray tracing is a technique that allows us to graphically
find the location of an image produced by a mirror or
lens.
The three rays normally used to determine image
locations are illustrated above. Only two are really
needed to define a point on an image.
Above we see two cases illustrating the formation of a
real image. Notice that the object and image are
interchangeable.
This diagram illustrates how a virtual image can be
formed with a concave mirror. Notice that the virtual
image is upright while the real image was inverted.
Ray tracing can also be used to determine image
location with convex mirrors. The rays used are the
same, but the image is always virtual, upright and
reduced in size.
The Mirror Equation and the Magnification Equation
The diagrams above are used to understand the magnification
equation and the mirror equation. In diagram (a) the two
triangles are similar since θi = θr, the angle with the principal
axis in both cases is 90°, and every triangle has a total of 180°.
Since they are similar, we can write:
-hi/ho = di/do
hi is negative since it is below the principal axis.
This is the magnification equation since magnification is
defined as the ratio of the image height to the ratio of the
object height. It is usually written with the negative sign on the
right side of the equation.
The mirror equation relates the focal length, the object
distance, and the image distance. It is:
1/f = 1/do + 1/di
For a concave mirror, the focal length is always positive and
the object distance is always positive indicating that they are in
front of the mirror. The image distance is positive if the image
is in front of the mirror or it is negative if the image is formed
behind the mirror.
Example
A concave mirror(R = 56.0 cm) is used to project the image of
a slide on a wall.The slide is 31.0 cm from the mirror and a
light shines through the slide. (a)How far from the wall should
the mirror be located to produce a clear image? (b) If the
picture on the slide is 0.95 cm high, what is the height of the
image? (c) How should the slide be oriented to produce an
upright image on the wall?
The same equations shown for concave mirrors can be used
with convex mirrors if we remember that the focal length of a
convex mirror is negative. Since a convex mirror is a diverging
mirror, the focal point is located behind the mirror. Distances
behind the mirror are considered negative.
Example
An object is placed 9.00 cm in front of a mirror. The image is
3.00 cm closer to the mirror when the mirror is convex instead
of planar. Find the focal length of the convex mirror.
P 768 Questions 3, 6, 7, 9, 10, 11, 13
P 769 Problems 2, 3, 6, 7, 9, 12, 16, 17, 19, 20, 22, 24