Video Transcript
Can the image produced by a convex
mirror be larger than the imaged object?
Seen from the side, a convex mirror
can look like this, where the rays of light approach the mirror from the right. All points on the surface of the
mirror are the same distance away from a point called the center of curvature. Between the mirror and the center
of curvature is another point called the focal point. The horizontal line joining these
two points is called the optical axis. Now we bring all this up because
these two points and the optical axis can help us answer this question. When this convex mirror produces an
image, we want to know if it’s ever possible for that image to be larger than the
object it’s an image of.
Say that this is our object, and
this could literally be any physical object. We can find out what the image of
this object looks like by tracing rays of light from the tip of the object. First, let’s consider a ray of
light that runs parallel to the optical axis. That ray will be reflected like
this, and we can trace it back and see that that trace passes through the focal
point. The other ray from our object is
one headed straight toward the center of curvature of our mirror. This ray will reflect backward
along the path it came. The top of our image will form
where these two traced lines intersect at this point here. Overall then, our image will look
like this. And we see that indeed it is
smaller than our object.
Our question, though, is asking if
it can ever happen that the image produced be larger than the object. Maybe, we might think, for some
differently sized object or a differently positioned object, the image would indeed
be larger. But let’s consider this. No matter where our object is, so
long as it’s on the right side of the mirror, and no matter how large or small our
object is, we know that the image of that object must appear somewhere along this
line that is traveling from the tip of the object to the center of curvature of the
mirror.
In the case of our object being
located here and having this size, we’ve seen that that point is right here. But then notice something about
this line. The line always slopes
downward. That means that by the time we pass
behind the mirror, whatever the height of our image will be, it must be less than
the height of the object. In fact, the same sort of thinking
applies to an object that looked, say, like this. A ray of light from the tip of this
object that’s traveling toward the center of curvature would look this way.
Once again, the tip of the image of
this object would lie somewhere along this line behind the mirror. Since this line is sloping toward
the optical axis, we can see the image will once again be smaller than the
object. We see then that in general, the
image produced by a convex mirror must be smaller than the object. Such an image is said to be reduced
in size. So for our answer, we’ll say that
no, the image produced by a convex mirror cannot be larger than the imaged
object.
