Video Transcript
The following figure shows a
nearsighted eye. If lens A is placed in front of the
eye, does the light focus nearer to or farther from the retina of the eye?
In this question, we see two
parallel light rays. We can also see an eye. The question states that the eye is
nearsighted. We can see that the light rays
enter the nearsighted eye and these rays cross paths at a point before the back of
the eye. Finally, the question shows a
convex lens, lens A, and concave lens, lens B, and asks whether placing lens A in
front of the eye would make the light entering the eye focus nearer to or farther
from the retina of the eye.
Let us think about what is meant by
focusing. Light rays are focused if they
converge at a point, called the focal point. The distance from a lens to its
focal point is called its focal length. We see that the two light rays do
converge at a point, the point before the back of the eye.
Let us think about what is meant by
retina. The retina of an eye is a part of
the eye that light must be focused on for the eye to see correctly. The retina is located at the back
of the eye. We can see that the eye in the
question does not focus the light rays shown at the retina of the eye.
Let us think about what is meant by
nearsighted. An eye is nearsighted if it can
correctly focus only light from nearby objects. A nearsighted eye cannot correctly
focus light from faraway objects. In the question, the two light rays
are parallel. Light rays from a faraway objects
are very nearly parallel. So we see that the question shows
an eye failing to correctly focus parallel light rays from a faraway object,
specifically focusing these light rays before the retina rather than at the
retina.
It is important to understand that
the initially parallel light rays eventually being focused must mean that when the
light rays enter the eye, the rays change direction so that they converge rather
than continue to travel parallel to each other after they enter the eye.
We can see then that the fact that
the light rays focus before the retina means that the eye changed the direction of
the light rays by too great an angle to make the rays converge at the retina. If the angle that the light rays
change direction by was less, these light rays would converge at the retina.
The question is asking whether
passing through lens A before entering the eye would change the paths of the light
rays that enter the eye so that they focus closer to the retina or farther from the
retina. To decide whether lens A can
produce this result, we need to understand the effect of lens A on the paths of the
parallel light rays from the object.
Recall that lens A is a convex
lens. A convex lens is also known as a
converging lens. This is because a convex lens will
cause incident parallel light rays to converge after they exit the lens. We can see that the eye itself must
act as a converging lens, as parallel light rays that enter the eye then
converge. Recall that the nearsighted eye
could not focus the incident parallel light rays at the retina, as the eye changed
the directions of the light rays too much. The eye had too small a focal
length to focus these rays at the retina. This means that for the eye to
focus these rays on the retina, the rays would need to be diverging before they
enter the eye.
We know that as lens A is convex,
it will make parallel rays that enter the lens converge after they leave the
lens. This is the opposite of what would
need to happen to the rays for the eye to make them converge at the retina. We conclude that placing lens A in
front of the eye will focus the light rays from the object farther from the
retina.
