Video Transcript
Fill in the blank. The focal length of a concave
mirror is the distance between the point on the surface that the optical axis passes
through and the blank. (A) Observer, (B) focal point, or
(C) center of curvature.
In this question, we are asked what
the focal length of a concave mirror is. First, let’s draw a diagram to
remind ourselves of how a concave mirror works. The mirror itself looks like
this. We can draw in the optical axis,
which is essentially the line of symmetry of the mirror. We can then label the center of
curvature of the mirror. This is the point that is the same
distance away from every point on the mirror.
Now, if some rays of light parallel
to the optical axis were incident on this mirror, they’d be reflected like this. Notice that the reflected rays
converge and pass through this point here. This is called the focal point of
the mirror. It’s where rays which are parallel
to the optical axis will be focused to. We can also draw in an observer
over here, who can see light rays which are reflected from the mirror.
Now, to answer this question, we’ll
need to recall the definition of focal length. The focal length of a mirror is the
distance between the mirror and the focal point, measured along the optical
axis. So, to complete the sentence given
in the question, we’d need to fill in the blank with “focal point.” That’s option (B). But let’s quickly think about the
other answer options just to make sure that we’re right.
Option (C) is center of
curvature. However, the distance between the
point on the surface of the mirror that the optical axis passes through and the
center of curvature, that’s this distance on our diagram, is called the radius of
curvature. We can see that this is not the
same thing as the focal length. So we can confidently say that
option (C) is not the correct answer.
Option (A) is observer. We can also rule this one out since
focal length is a property of a given mirror. So it can’t depend on the position
of an observer. The distance between the center of
the mirror and the observer doesn’t really have a special name.
The correct answer then is option
(B). Our completed sentence reads “The
focal length of a concave mirror is the distance between the point on the surface
that the optical axis passes through and the focal point.”