Video Transcript
The following figure shows parallel
light rays reflecting from a convex mirror. If the reflected ray of an incident
ray travels the same path as the incident ray, which of the following must an
incident ray do? (A) Pass through the center of
curvature of the mirror, (B) pass through the focal point of the mirror, (C) travel
along the optical axis of the mirror.
To answer this question, we need to
recall what the center of curvature, focal point, and optical axis for a convex
mirror are.
Let’s draw ourselves a convex
mirror. A convex mirror can be described as
a portion of a sphere that’s been sliced away. The center of this sphere is known
as the center of curvature. The line that passes from the
center of the mirror’s surface through to the sphere’s center is known as the
optical axis. Midway between the front of the
mirror and the center of curvature is the focal point.
Now that we have recalled these
features of a convex mirror, we can now look at the figure given in the
question. The figure has already labeled the
center of curvature. So let’s add in the labels for the
focal point and optical axis onto this figure. We notice that the center of
curvature and focal point of the mirror are located inside the mirror, while the
reflected and incident rays are located outside of the mirror. Since the incident ray will not
pass through the mirror, this means that the incident ray will not pass through the
center of curvature or the focal point of the mirror. Therefore, we can eliminate options
(A) and (B).
This leaves us with option (C). Any incident ray that travels along
the optical axis of a convex mirror will hit the point at the front of the mirror
and be reflected back along its incoming path. This means that option (C) is the
correct answer. The incident ray will travel along
the optical axis of the mirror if the reflected ray travels the same path as the
incident ray.
