### Video Transcript

The diagram shows a concave
lens. Light rays pass through the lens in
the horizontal direction. Which line shows the optical axis
of the lens?

In this question, we are given a
diagram that shows us a concave lens with five different lines passing through
it. We are asked to find which line
shows the optical axis of this lens.

First, let’s recall what we know
about the shape of concave lenses and how they interact with light rays. A concave lens is a lens with a
curved surface that is thickest along the edges and thinnest at the middle of the
lens. We can create this shape by taking
a cylinder and orienting its circular faces along the horizontal axis. If we then draw two spheres along
the side of the cylinder, like we’ve shown here, and remove the overlapped material
from the cylinder, we are left with a shape that makes a concave lens.

Next, to help us determine the
optical axis, let’s take a look at the center of these spheres here. These two points in the center are
called the centers of curvature because they are an equal distance from every point
along the edge of their respective spheres.

If we draw lines from the centers
of curvature to the edge of each sphere, then we have found our radius of curvature
for these spheres. The radius of curvature will be the
same length, no matter which point on the edge it is pointing towards, since the
distance from the center of curvature is the same at all points.

Notice that these centers of
curvature line up with the center of our lens. In fact, if we connect these
points, we get a line that will go through the geometric center of this lens. We call this line the optical axis
of our lens, which is what our question is asking us to find in the given
diagram.

Let’s compare our two images. We are looking for the optical axis
of this lens, which is the line that passes horizontally through the center of the
lens. We can see that all five lines are
passing through the center of our lens. But most of them are traveling
through at an angle. Only line number four passes
through the center and is also horizontal, which means this is our optical axis. Therefore, line four is the correct
answer.