Formation of Images by
For an object infinitely far away (the sun or starts), the rays
would be precisely parallel.
If a mirror is small compared to its
radius of curvature, so that the reflected
rays make only a small angle upon
reflection, then the rays will cross each
other at a single point, or focus.
The principal axis of a mirror is defined as the
straight line perpendicular to the curved
surface at its center.
The point F, where the rays parallel to the
principal axis, come to a focus, is called
the focal point of the mirror.
The distance between focal point and the
center of the mirror is called the focal
length, f, of the mirror.
Another way of defining the focal point is
to say that it is the image point for an
object infinitely far away along the
Finding the Image Position for a
-ray 1 is drawn parallel to the axis; therefore it must pass
along a line through F;
-ray 2 is drawn through F, as result is must reflect into parallel
to the principal axis ray;
-ray 3 is chosen to be perpendicular to the mirror, and so is
drawn so that it passes through C, the center of curvature; it
will be reflected back on itself.
1 1 1
do di f
The lateral magnification, m, of a mirror is
defined as the height of the image divided by
the height of the object:
The Sign Convention
-the image height hi is positive if the image is
upright, and negative if inverted, relative to the
-di and do are both positive if image and object are
on the reflecting side of mirror, but if either image
or object are behind the mirror, the corresponding
distance is negative.
1. You hold a small light bulb directly in front of a concave mirror
beyond the mirror focal point. Is it possible for two rays leaving
the light bulb to intersect after reflecting from the mirror? Is the
bulb image real or virtual? Explain.
2. Can the image produced by a convex mirror ever be larger than
the object? Why?
3. Most of us find that we really have to strain our eyes to focus on
objects located close to our noses. You hold two mirrors 1 foot
in front of your face. One is a plane mirror, and the other is a
concave mirror with a 3-inch focal length. In which case are you
more likely to have tp strain your eyes to see the image of your
1. What type of mirror would you use to produce a
magnified image of your face/
2. The image produced by a convex mirror is always closer
to the mirror than the object. Then why is it that the
convex mirrors used on cars and trucks often have the
warning: “Caution: Objects Are Closer Than They
Appear” printed on them?
3. What are the size and location of the image of your face
when you hold your face very close to a concave mirror?
How do the size and location change as you move away
from the mirror?
Index of Refraction
The ratio of the speed of light in vacuum
to the speed of light v in a given material
is called the index of refraction, n of the
If the light enters the medium where the
speed of light is less, it bends toward the
If light travels from one medium into a
second where its speed is greater, the ray
bends away from the normal.
n1 sin1 n2 sin 2
Total Internal Reflection
Important: total internal reflection can
occur only when light strikes a boundary
where the medium beyond has a lower
index of refraction.
Total Internal Reflection: