Video Transcript
The following figure shows an
object and its virtual image that is formed by light rays reflected from a convex
mirror. If the object is moved away from
the mirror, how does the size of the image change? Is it (A) the image becomes
smaller, (B) the image becomes larger, or (C) the size of the image does not
change?
The size of the virtual image can
be determined by drawing ray diagrams for these two scenarios. Here we have an object that extends
above the optical axis. We will consider just two rays that
come off the top of the object. One of these rays travels parallel
to the optical axis. The first light ray will be
reflected so that if we trace the reflected ray backward, we cross through the focal
point. The second one we’ll consider moves
straight towards the center of curvature of our mirror. This second ray will be reflected
straight backward along the path it came from. The point of intersection of the
dashed lines shows where the image of this part of our object forms. The same method can be applied for
the bottom of the object, and the virtual image is formed.
Now, let’s move the object further
away from the convex mirror and apply the same methods to form the virtual image for
this case. The first light ray that travels
parallel to the optical axis will be reflected so that if we trace the reflected ray
backward, we cross through the focal point. The second ray moves straight
towards the center of curvature of our mirror and will be reflected straight
backward along the path it came from. Drawing in the incident and
reflected rays for the bottom of the object and we can determine the updated virtual
image from the points of intersection.
So now we can compare the image
sizes from these two scenarios. As can be seen here, when we move
the object away from the mirror, the image size becomes smaller. Therefore, the correct answer is
option (A).
