### Video Transcript

The diagram below shows five
concave lenses. Which lens has the greatest radius
of curvature?

This question asks us which of the
lenses shown has the greatest radius of curvature. We can see that all these lenses
are concave lenses.

First, let’s remember that a
concave lens can be formed like this, with a cylinder and two spheres in such a way
that the intersection of all of them forms the concave lens. The radius of each of the spheres
is the radius of curvature of the concave lens. The larger the radius of the
spheres, the larger the volume of the spheres will be, and so the thinner the lens
is at the top and the bottom. That is, a larger radius of
curvature means a concave lens that is thinner at the top and bottom. Or we could equally flip that
statement around to say that a concave lens that is thinner at the top and bottom is
a lens that has a larger radius of curvature.

Let’s now look at the five lenses
we’re given in the question. We can draw in one of the spheres
that forms the concave lens for each of the five lenses we are given. Then, using these spheres, we can
easily identify the radii of curvature for lenses 1, 2, and 5. Lenses 3 and 4 are clearly formed
from spheres that are larger than 1, 2, and 5. We cannot easily fit the full
spheres on screen in these cases to add the radii of curvature. However, we can note that lens 4 is
the thinnest at the top and bottom and the part of the sphere we have drawn in for
this lens appears less curved than that for lens 3, and indeed all the other
lenses.

So the concave lens made up from
the largest spheres, or the lens with the largest radius of curvature, is lens
4. Therefore, our answer to the
question is lens 4.