Video Transcript
The following figure shows the
formation of an image by a convex mirror. The object is moved from its
initial position to a position nearer to the mirror. How is the size of the image
affected?
The diagram in the question shows
two positions of the object and one position of the image. There are some things that are
useful to recognize from the diagram in the question. The most important thing that is
useful to recognize is that the top of the image appears where two colored dashed
lines cross each other. One of these lines is a line that
passes from the focal point of the mirror to the point on the mirror from which a
light ray is reflected that initially traveled from the top of the object to the
mirror, parallel to the optical axis. One of these lines is a line that
passes from the center of curvature of the mirror to the top of the object. This is the direction in which a
light ray from the top of the object would travel if it was to travel directly
towards the center of curvature.
The relationship between the
position of the top of the object and the position of the top of the image is
actually true for all points on the object and the image. And it is true whatever the
distance between the object and the image is.
Looking at the lines shown in the
diagram, we see that the image shown is the image that is produced when the object
is moved closer to the mirror. We see that at this position, the
base of the object seems to be very close to the surface of the mirror, possibly
actually touching the mirror. We also see that the image is
slightly smaller than the object. As the image shown indicates the
size of the image when the object is very close to the mirror, it is necessary to
consider what the size of the image would be if the object was further from the
mirror.
Considering what would happen if
the object was further from the mirror, there are some further important things to
recognize. We notice that the incident rays
are parallel to each other and to the optical axis of the mirror. We also notice that when the object
is moved away from the mirror, the object moves along the optical axis. If the object was at the position
shown by the dashed rectangle, the light ray traveling from the top of the object
traveling parallel to the optical axis falls on the mirror at the same point as it
did when the object was closer to the mirror.
As the light ray is incident at the
same point as it was before and travels in the same direction that it did before,
the light ray is reflected in the same direction as it was before. We see then that the dashed line
that passes through the focal point of the mirror has the same direction before and
after the object moves. However, when the object moves, the
direction that a light ray from the top of the object must travel in to travel
directly toward the center of curvature of the mirror changes. As this line has changed direction,
where this line crosses the line that passes through the focal point also
changes.
We see that the point where these
lines cross is closer to the optical axis. This shows that the top of the
image is closer to the optical axis when the object is further away from the
mirror. This means that the image is
smaller when the object is further away from the mirror. We can see then that moving the
object towards the mirror must make the image larger.
