Download Convex Mirrors

Buggé: Optics 5
Convex Mirrors
5.1 How do those four special rays we drew for concave mirrors look for a convex mirror?
1) A ray that leaves the object and strikes the mirror parallel to the optical axis.
2) A ray that leaves the object and looks like it would go through the focal point of the mirror.
3) A ray that strikes the mirror at an angle at the optical axis.
4) A ray that leaves the mirror from the object and goes through, or looks like it came from, the center of the
mirror.
5.2 Try it yourself
Patrick stands 3 meters from a convex mirror with a focal point of -1.5m.
a) Draw the ray diagram (use the strategy from last class!) and describe his image below.
b) How far away should the image be from the mirror? Is your math consistent with your ray diagram?
Buggé: Optics 5
5.3 Try it yourself
Patrick moves closer to the mirror and is now standing 1 m from the same mirror.
a) Draw the ray diagram for the situation and describe his image below.
b) How far away should the image be from the mirror? Is your math consistent with your ray diagram?
5.4 Magnification
What is the magnification of Patrick’s image in problem 3? Is your math consistent with your ray diagram?
5.5 Represent and Reason
We have a tendency to relate distance with size – if something is smaller than expected, one would think it is far
away. If larger than expected, one would think that it is very close.
a) Why are “objects in mirror closer than they appear?”
b) Why are passenger side mirrors convex?
5.6 Represent and Reason
Can a convex mirror produce an inverted image or a real image? If so, draw the ray diagram that shows how
this is possible. If not, explain why.
Buggé: Optics 5
Homework
5.7 Regular Problem Locate the position, orientation, and type of image formed by an upright object held in
front of a convex mirror of focal length (-50) cm. The object distance is 100cm. Include a ray diagram in your
answer.
5.8 Regular Problem Locate the position, orientation, and type of image formed by an upright object held in
front of a convex mirror of focal length (-50) cm. The object distance is 25cm. Include a ray diagram in your
answer.
5.9 Regular Problem Locate the position, orientation, and type of image formed by an upright object held in
front of a convex mirror of focal length (-5) cm. The object distance is 1cm. Include a ray diagram in your
answer.
5.10 Regular Problem Locate the position, orientation, and type of image formed by an upright object held in
front of a convex mirror of focal length (-2.05) cm. The object distance is 22.2 cm. Include a ray diagram in
your answer.
5.11 Regular problem Archimedes was known to burn enemy ships by starting a fire with a mirror. Was it a
concave or a convex mirror? Determine the focal length of the mirror Archimedes might have used to burn
ships that were 150 m away. Justify your answer.
5.12 Regular problem You wish to order a mirror from a scientific supply company. You want to use the
mirror while shaving or applying makeup. The mirror should produce an image that is upright and magnified by
a factor of 2.0 when held 15 cm from your face. What type and focal length should you order?
Buggé: Optics 5
Need some help?
Focal point of a concave mirror: The point where rays parallel to the main axis meet after the incident rays
reflect off the mirror. The focal distance is f = +C/2 on the side of the mirror from which the light is incident.
Focal point of a convex mirror: The point from which rays parallel to the main axis seem to diverge after the
incident rays reflect off the mirror. The focal distance is f = –C/2 on the opposite side of the mirror from which
the light is incident.
Mirror equation:
1 1 1
+ =
do d i f
Where do is the distance from the object to the mirror; di is the distance from the image to the mirror, and f is the
focal distance. The object distance and the focal length are positive. A positive image distance indicates a real
image on the same side as the incident light; a negative image distance indicates a virtual image on the opposite
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side from the incident light.
Magnification Equation:
hi
d
=− i
ho
do
An object often becomes magnified when reflected in a mirror where M is the magnification, hi is the high of
the image, ho is the height of the object, di is the distance from the image to the mirror, and do is the distance of
the object to the mirror. Note: The height of an inverted image is negative.
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M=
The sign conventions for the given quantities in the mirror equation and magnification equations are as follows:
f is + if the mirror is a concave mirror
f is - if the mirror is a convex mirror
di is + if the image is a real image and located on the object's side of the mirror.
di is - if the image is a virtual image and located behind the mirror.
hi is + if the image is an upright image (and therefore, also virtual)
hi is - if the image an inverted image (and therefore, also real)