The ray diagram below shows
different paths taken by parallel rays after they reflect off a convex mirror. Which one of the paths is
correct? (A) Path 1, because a convex mirror
will not focus the incident light at a point. (B) Path 2, because a convex mirror
will focus the incident light at a point.
In this problem, we’ve been given a
convex mirror and rays of incident light that are parallel to the optical axis of
the mirror. Both of these rays are initially
traveling along the same path. Hence we’ve been told they’re
parallel. One of these rays is reflected off
the mirror along path 1, and the other is reflected along path 2. But only one of these correctly
shows how a light ray actually reflects off a convex mirror. We need to figure out which one
To answer this question, let’s
remember an important fact about convex mirrors. Let’s recall that any ray of light
that is traveling parallel to the optical axis of a convex mirror will be reflected
off the mirror in a very specific way. We can trace backward the reflected
ray of light to see that it appears to come from this point here on the optical
axis. This point is known as the focal
point. And any other incident ray of light
that is parallel to the optical axis will also be reflected so that it appears as if
the reflected ray is coming from the focal point.
It’s important to remember though
that reflected rays only appear to be coming from the focal point. In reality, they are all being
reflected off in different directions from the surface of the mirror, and so are not
all being focused at one point after being reflected.
Knowing this, we can see that our
incident ray of light cannot be reflected along path 2, because if we trace this
path back, then it does not cross the optical axis on the other side of the
mirror. If we do this for path 1 though, we
see that this is exactly what we’re looking for.
Our final answer is option (A). The light ray is reflected along