Video: Identifying the Optical Axis of a Semicircular Object

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

02:18

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.

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