Video Transcript
The diagram shows a curved object
and some lines that could be the optical axis of the object. Which line correctly represents the
optical axis?
Looking over at our diagram, we see
this curved object and these five lines, I, II, III, IV, and V, which are all
candidates for being this object’s optical axis. To figure out which one is, let’s
start by recalling the definition of the optical axis.
The optical axis of a spherical
lens or mirror is an imaginary line that passes through its center of curvature, and
it also divides the object in half. Now, when we talk about a spherical
lens or mirror, we’re speaking of an optical element, where at least one of its
surfaces is part of a sphere. For example, this spherical surface
of our object is part of this larger sphere we’ve sketched in. And the sketch now helps us
identify what the center of curvature for this particular object is. It is the point at the center of
this sphere.
Our definition says that the
optical axis passes through this point. But we can see that many different
lines could pass through this point. So, we need to be more
specific. This is where the second part of
our definition comes in. That the optical axis passes
through the center of curvature and it divides our optical object in half. The line that meets both of these
conditions is sketched in in pink. And this is the optical axis for
this spherical object.
Getting back to our problem
statement, it tells us that the object we’re working with is a curved object. Note that it doesn’t say a
spherical object. So, we’re not confident that this
part of our object’s surface is part of a larger sphere. That said, we can consider the
second condition for an optical axis. That it divides whatever our object
is in half.
As we look over the five lines, I,
II, III, IV, and V, we see that only one of them meets this condition. Only line V divides the object in
half. And further, we can see that if
this object is indeed spherical, which it maybe, then, indeed, line V would pass
through the center of curvature of this object. We don’t know exactly where that
center is, but we can see that it’s somewhere along line V.
This indicates that it’s line
number V that correctly represents the optical axis of this curved object.
