Optics
Reflections/Mirrors
What do we see?
Law of Reflection
Properties of Spherical Mirrors
Ray Tracing
Images and the Equations
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Optics
Reflections/Mirrors
2
Optics
Reflections/Mirrors
All reflected rays bounce in such a way as to follow the law of reflection.
Law of Reflection
θr
θi
r  i
Where the rays
appeared to have
crossed is where we
see the image.
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Optics
Reflections/Mirrors
If only one reflected ray hits my eye, I will see the image.
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Optics
Reflections/Mirrors
For some parts of an object the reflected ray never hits the eye.
Any part of the object
on this side of the red
line is not seen by the
eye.
Any part of the image
on this side of the red
line is not seen by the
eye.
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Optics
Reflections/Mirrors
For all reflected light rays, the angle of incidence θi is equal to the angle
of reflection θr.
The eye sees the point from which the light originated as though it were
in a straight line from the angle of the reflected ray.
The eye will not see the reflection of any point on the object unless one
of the rays originating from that object strikes the mirror and reflects into
the eye.
The eye will not see any part of an object for which all rays approaching
the eye hits the back of the mirror.
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Optics
Reflections/Mirrors
The law of reflection states that:
The incident ray, the reflected ray and the normal to the mirror all lie in the
same plane.
The angle of reflection equals the angle of incidence.
θi
θr
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Optics
Reflections/Mirrors
For a spherical mirror, rays that start at the center point will go back through
the center point.
This is because the normal to any point on the spherical surface of the
mirror points to the center of the sphere.
C
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r
Optics
Reflections/Mirrors
The principal axis is any line which crosses through the center point of the
mirror and touches the mirror itself.
The most commonly used axis is the one that bisects the mirror.
C
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Optics
Reflections/Mirrors
For any mirror, the focal point is defined as the point where parallel rays
that are near to the principal axis reflect to a point.
Any rays that originate at the focal point will reflect parallel to the principal
axis.
C
F
f
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Optics
Reflections/Mirrors
There are two types of spherical mirrors: concave (converging) and convex
(diverging).
Parallel rays reflecting off a convex mirror do not reflect to a point. Instead
they diverge in such a way as to appear to be coming from the focal point.
F
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C
Optics
Reflections/Mirrors
Although any ray may be traced to find out where an image point is, there
are three principal rays that make the job easier.
1. Parallel Ray: Comes in parallel to the principal axis and goes out through
the focal point.
2. Focal Ray: Comes in through the focal point and goes out parallel to the
principal axis.
3. Radial Ray: Comes in through the center point and retraces its path.
C
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F
Optics
Reflections/Mirrors
Although any ray may be traced to find out where an image points is, there
are three principal rays that make the job easier.
1. Parallel Ray: Comes in parallel to the principal axis and goes out as
though it came from the focal point.
2. Focal Ray: Comes in toward the focal point and goes out parallel to the
principal axis.
3. Radial Ray: Comes in toward the center point and retraces its path.
F
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C
Optics
Reflections/Mirrors
Images are real if all of the light rays pass through them. Otherwise they
are virtual.
Real images are inverted, virtual images are upright.
For mirrors, real images are found on the same side of the mirror as the
object. Virtual images are not.
Images may be smaller or larger than the object.
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Optics
Reflections/Mirrors
f, do , ho and di are all positive
and hi is negative.
C
F
F
C
f and di are negative and do, ho
and hi are positive.
Focal length (f), object distance (do) and image distance (di) switch signs as
you move across the mirror.
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Heights (ho for object and hi for image) are positive if the image or object is
upright and negative if they are inverted.
Optics
Reflections/Mirrors
The same equation may be used to find the image distance, object distance
or focal length for both types of spherical mirrors. This is called the mirror
equation.
1
1 1


f d o di
The magnification equation may be used to find the height of the image or
object or to find the magnification of a mirror.
hi
di
m 
ho
do
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