### 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.