Video Transcript
The diagram shows five light rays
that will pass through a thin concave lens. Which of the light rays will not
change direction as it passes through the lens?
In this question, we are given a
diagram showing a concave lens and five light rays that will pass through it. We are asked to figure out which
ray will not change direction as it passes through the lens. Let’s begin by refreshing our
memories about what concave lenses are and how they interact with light rays.
A concave lens is a lens with
curved faces that are thickest at the edges and thinnest in the middle. We can create this shape using a
cylinder that is being overlapped by two spheres on its circular faces, like seen
here. If we remove the material that is
overlapped by the spheres, we are left with the shape of a concave lens. A two-dimensional cross section of
the lens looks like a rectangle, from each side of which an identical part of a
circle has been removed. The centers of these circles are
the centers of curvature of the lens. The centers of curvature are at
equal distances to every point along the circumferences of their circles. This distance is called the radius
of curvature. For a circle, the radius of
curvature is equal in all directions.
If we connect the two centers of
curvature with a line, the line defines the optical axis of the lens. The line passes through the center
of the lens. The point at the center of the lens
is special in that a light ray that enters the lens center and passes through the
lens will exit the lens traveling in the same direction that it was traveling in
when it entered the lens. This is true for light rays that
enter the lens center at any angle to the optical axis.
Rays that enter the lens parallel
to the optical axis but not along the optical axis will change direction, diverging
from the center of the lens. If the paths of light rays exiting
the lens are traced back through the lens, the lines traced back all originate from
the same point. This point is called the focal
point of the lens. The distance from the focal point
to the center of the lens is called the focal length. And because concave lenses are
symmetric, there’s a focal point on each side of the lens. Both focal points have equal focal
lengths.
Now that we remember what concave
lenses are, as well as their centers of curvature, optical axes, and focal points,
let’s take another look at the diagram we are given. Looking at the rays shown in the
question, we can see that they are all traveling parallel to the optical axis. But ray one and ray two are above
the optical axis, and ray four and ray five are below the optical axis. This means that rays one, two,
four, and five will all change direction and will appear to start at a focal point
of the lens. Only ray three passes through the
center of our lens, which means it will not change direction when it passes through
the lens. Therefore, the middle ray, ray
three, is the correct answer.
