### Video Transcript

The diagram shows a semicircular
object and some lines which could be the optical axis of the object. Which line correctly represents the
optical axis?

All right, so here we have this
diagram. And we see the semicircular object
with these different dashed lines marked out. Each one of these dashed lines is a
candidate for what’s called the optical axis of this object. We want to figure out which one of
them, I, II, III, IV, or V, is the actual optical axis. We can start by recalling the
definition of the optical axis of an object.

The optical axis of a spherical
lens or mirror is an imaginary line that passes through its center of curvature. And it divides the object in
half. So if we start out with a spherical
lens or mirror, a spherical object like this, the reason we say that this object is
spherical is because it has at least one curved surface that’s part of a sphere. For the object we’ve drawn in here,
that surface is this part of the object.

Now, our definition of the optical
axis involves something called the center of curvature. That point is simply the center of
the sphere that we’ve drawn in. We would say that this point is the
center of curvature for this spherical object. Our definition tells us the optical
axis passes through this point, the center of curvature. We can see though that it doesn’t
totally define what the optical axis is. Many different lines could pass
through that point. But if we continue on in our
definition, we see that this line also divides the object in half.

If we were to draw in a line that
passes through this point and also divides the spherical object in half, that line
would look like this. It’s an imaginary line that’s
called the optical axis for the spherical element. And this brings us back to our
diagram. If we consider our semicircular
object here, we can complete the sphere that this semicircular object is a part
of. And we see that the center of that
sphere, which is the center of curvature of this object, is right at this point
here. As it turns out, that’s all we need
to know to realize which of these five lines represents the optical axis of this
object. The only line that passes through
the center of curvature of this object is line III.

Notice, though, that this line does
divide the object in half, so it meets the second condition of an optical axis. For this reason, we can say that
it’s line III that correctly represents the optical axis of the semicircular
object.