Video Transcript
How many foci does a convex lens
have?
In this question, we are asked to
take a convex lens and figure out how many foci it has. First, it will be helpful to
remember what a convex lens is, and then we can figure out how many foci they
have.
Let’s begin by taking a look at the
shape of a convex lens as viewed from the side. This shape can be made by
overlapping two circles. The overlap seen here is the same
shape as a convex lens. The convex lens has two curved
sides with the edges, the top and bottom of this cross section, being the thinner
part of the lens and the thickest part in the middle. Notice that convex lenses are
symmetrical. They can be split along the
horizontal or vertical axis. And in either case, the halves of
the lens on either side of the split have the same shape, but facing in opposite
directions.
Now, back to the overlapping
circles, seeing them as helpful in finding the centers of curvature for a convex
lens, recall that a center of curvature is the point that is an equal distance to
every point on the edge of one of the circles that determines the shape of the
lens. In a circle, the center of
curvature is in the exact center. And if we connect the center of
curvature to a point on the edge of the circle, we will have what is called the
radius of curvature. If we connect our centers of
curvature with a line, we will have the line called the optical axis. The optical axis is the line
through the center of our lens.
One property of convex lenses is
that if a ray of light passes through the center of the lens, it will pass straight
through the lens without changing direction. If a ray of light hits a convex
lens at any other point, that ray will change direction as it passes through.
Because this question is asking us
about the foci of convex lenses, let’s refresh our memory about what foci means. Foci is the plural of focus. We already know that if a ray of
light passes through the center of the lens, it does not change direction. This includes rays of light that
pass right along the optical axis. But what about rays of light that
pass through the lens parallel to the optical axis but not along the optical
axis? In this case, all the rays of light
that pass into the lens parallel to the optical axis will be focused and converge on
a single point on the other side of the lens. This point where the rays of light
cross each other is called the focal point.
So, now that we know what a focal
point is, let’s go back to the shape of the convex lens and try to figure this
question out. We have seen what happens when
light rays travel in one side of the lens and focus at the focal point. But what if we sent light rays in
through the other side of the lens?
Well, because convex lenses are
symmetrical about the vertical axis, we would expect these light rays to be focused
at another focal point on the other side of the lens, the same distance away as the
first focal point we found. And that is exactly what we
see. So this means that each convex lens
has two focal points, or foci, one on either side of the lens. Two foci is the correct answer.
