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Question Video: Comparing the Radii of Curvature of Two Concave Lenses Science

The diagram shows two concave lenses. Which lens has the greater radius of curvature?


Video Transcript

The diagram below shows two concave lenses. Which lens has the greater radius of curvature?

Here, we are given a diagram of two concave lenses with corresponding circles showing their curvature. We are asked to take a look at them and figure out which of the two lenses has the greater radius of curvature. To figure this out, we should remember what concave lenses are and what the radius of curvature is.

A concave lens has curved surfaces on two of its faces and is thicker along the edges and thinner in the middle. When we think about a concave lens shape, we should start by imagining a cylinder with its circular sides aligned horizontally. In order to turn this shape into a concave lens, we can bring in two spheres, which we’ll represent as circles. And if we remove the material from the cylinder that is overlapped by the spheres, we get a diagram of a concave lens very similar to the one given to us in this problem.

Now that we have this diagram, let’s define some parts of it. We have the lens in the center, with two circles touching its curved surfaces. If we take points at the very center of these circles such that the distance from those points is equidistant from any point on the circles, then we can call these points the centers of curvature. If we connect these two points with a line, it will travel directly through the center of our lens. Such a line we call the optical axis of the lens. Each center of curvature is equidistant to every point on the edge of its circle. And that distance, from a center of curvature to the edge of the circle, is called the radius of curvature. This distance will be the same regardless of where on the edge we move to as long as we begin at the center of curvature.

Now we know what the radius of curvature is and how we find it by drawing a line from the center of a circle. Let’s go back to the diagram from the question and see what the radius of curvature is for lens one and two. We can mark the centers of curvature for each circle with a point in the exact center and then draw lines straight up from those points to the edges of the circles. This gives us the radius of curvature for each of these lenses. After doing this, we can see that the radius of curvature for lens one is a bit larger than the radius of curvature of lens two. The circle for lens one is much bigger than the circle for lens two. So it should stand to reason that it will also have a bigger radius and, thus, radius of curvature.

Therefore, the correct answer for which lens has the greater radius of curvature is lens one.

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