Video Transcript
The following figure shows a
farsighted 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 light
rays that are diverging from a point. We can also see an eye. The question states that the eye is
farsighted. We can see that the light rays
enter the farsighted eye and these rays cross paths at a point behind 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 can see that the two light rays
do converge to a point, the point behind the back of the eye.
Let us think about what is meant by
retina. The retina of an eye is 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
farsighted. An eye is farsighted if it can
correctly focus only light from faraway objects. A farsighted eye cannot correctly
focus light from nearby objects. In the question, the two light rays
diverge from a point. The point from which the light rays
diverge is the position of an object. The less the distance between the
object and the eye, the greater the divergence of the light rays from the object
that enter the eye.
So we see that the question shows
an eye failing to correctly focus light rays diverging from a nearby object,
specifically focusing these light rays behind the retina rather than at the
retina. It is important to understand that
the initially diverging 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 diverge after they enter the eye.
We can see then that the fact that
the light rays focus behind the retina means that the eye changed the direction of
the light rays by too small an angle to make the rays converge at the retina. If the angle that the light rays
change direction by was greater, the light rays could converge at the retina. Another way of describing this is
that if the focal length for the eye was decreased, these light rays could 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
diverging light rays from the object.
Recall that lens A is a convex
lens. This is because a convex lens will
cause incident parallel light rays to converge after they exit the lens. Parallel light rays neither diverge
nor converge. Causing parallel rays to converge
is the opposite of causing the rays to diverge. We can see then that a convex lens
can be considered antidivergent, in that it does the opposite of increasing the
divergence of light rays. If we think of a convex lens as
reducing the divergence of light rays, we can deduce that if divergent light rays
enter a convex lens, the rays will diverge less after they exit the lens.
Recall that the farsighted eye
could not focus the incident diverging light rays of the retina, as the eye did not
change the directions of the light rays enough. The light rays were changed from
diverging to converging, but the eye had too great a focal length to focus these
rays at the retina. If the light rays that enter the
eye are made to be less divergent by the correct amount before they enter the eye,
then the focal length of the eye would be sufficient to focus the rays at the
retina.
We know that as lens A is convex,
it will reduce the divergence of the light rays from the object. Therefore, placing lens A in front
of the eye could change the path of light rays so that they converged at the
retina. Even if lens A did not exactly
focus these rays at the retina, the rays would be focused nearer to the retina than
if lens A was not used. We conclude that placing lens A in
front of the eye will focus the light rays from the object nearer to the retina.
