### Video Transcript

The diagram shows a thin convex
lens. The lens is symmetrical. The point marked P is one of the
foci of the lens. Using the grid, determine which of
the points I, II, III, or IV is the other focus of the lens.

Here, we are given a diagram
showing a grid with a thin convex lens, a focal point labeled P, and four other
points on the other side of the lens. We are asked to use the grid to
determine which point is the other focal point of the lens. We are also told in the question
that the lens we have here is symmetrical. That means that if we cut it in
half along the vertical or horizontal axis, we would have two halves that are
identical.

If we look at the shape of a convex
lens viewed from the side, we can see that it is made up of the overlap of two
circles put on top of each other, like seen here. The shape of the convex lens allows
it to focus rays of light to a single point called the focal point. We can see how this works by
looking at light rays traveling parallel to the optical axis through a lens and
noticing that they all converge to a single point on the other side of the lens. This is the focal point of our
lens. And because convex lenses are
symmetrical, this will also happen if we send light rays through the other side in
the same manner. Only this time the light rays will
converge to the focal point on the other side. Notice how these two points are the
same distance away from the lens.

Now, back to our question and
diagram, take a look at the lens and point P. And let’s measure the distance from
the center of the lens to that point. We can see that point P is five
squares away from the center of the lens. This means that we would expect the
focal point on the other side to be the same distance away. So let’s find which point
corresponds to it.

Starting at the center of the lens
and moving five squares to the left, we find that point II is that distance
away. Therefore, point II is the point
where the other focus would be. So point II is the correct
answer.