Video Transcript
Which of the following is the
correct definition of the focal length of a lens? (A) The focal length of a lens is
the distance between the center of the lens and one of its centers of curvature. (B) The focal length of a lens is
the distance between its two foci. (C) The focal length of a lens is
the distance between its two centers of curvature. (D) The focal length of a lens is
the distance between the center of the lens and one of its foci.
Let’s start by thinking about what
we know about lenses and making sure we understand all the terms used in the
question. Let’s draw a concave lens from the
side. We know that the middle of a
concave lens is thinner than the edges, and each side is curved. These curves are parts of circles,
which we can draw in like this.
The centers of these circles are
called the lens’s centers of curvature. Each lens has two centers of
curvature, one on each side of the lens. Imagine now the centers of
curvature are joined by a line. This line is what we call the
optical axis. When parallel rays of light enter a
concave lens, the lens causes them to diverge, or spread out. If we trace these diverging rays
backwards, ignoring the lens, then we see that they seem to meet at a point behind
the lens. We call this imaginary point the
focal point of the lens.
Although the light rays don’t all
actually pass through this point, it appears that the light rays exiting the lens
are originating from the focal point. Now, of course, light can travel
both ways through the lens. And so, there are two of these
focal points, one on each side of the lens. The focal length is the distance
between the center of the lens and either of the focal points. That is, the focal length of the
lens is equal to either of these two distances shown in orange.
So, let’s now go back to the
question. We need to identify the correct
definition for the focal length of a lens. Let’s look at what our options
are. Option (A) states that the focal
length is the distance between the center of the lens and one of the centers of
curvature. But we know that this is not
correct. Although a lens does have two
centers of curvature, they do not define the focal length. So, we can rule out option (A).
We can also rule out option (C) for
the same reasons. Option (C) states that the focal
length is the distance between the two centers of curvature, but we know that that’s
not right.
Option (B) states that the focal
length is the distance between the two focal points, without any mention of the
center of the lens. We know that the focal length is
measured from the center of the lens. And so, we know that option (B) is
wrong.
Finally, option (D) states that the
focal length is the distance between the center of the lens and one of its focal
points, or foci. That’s great because this is what
we know to be the correct definition of the focal length.
So, we have our answer. Option (D) is the correct
choice. The focal length of a lens is the
distance between the center of the lens and one of its foci.
