Video: Identifying the Optical Axis of a Curved Object

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?

02:09

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.

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