Here is a simulation of a near-sighted eye. The
lens at the front of the eye is "too strong", and is converging
the light before the back of the eye (so, the light that gets to
the back will be out of focus - fuzzy - for distant objects). To correct
for this type of vision, we put a diverging lens into the eyeglasses -
conceptually, this spreads the light out before it gets to the eye-lens,
and thus when the eye-lens converges it, it will now converge on the back
fo the eye for proper focus.
There is another interesting view of this
system ... consider the nearpoints and far points of the human eye. Eyes
that don't need any correction have a near point of about 25 cm, and a far
point very far away (essentially infinite). Near-sighted people have a far
point that is dramatically shorter - for example, suppose it was 40 cm
from the eye ... so that near-sighted eye "can't" see anything
beyond about 40 cm (the distance would change depending on how
near-sighted the person is). So, what is that diverging lens doing ...
look at the light coming from the diverging lens .. what does the
converging lens think about that light .. it thinks it is coming from an "object"
that is much closer to the lens than the original object .. and if it is
inside the far point .. the eye-lens can now resolve that image
properly!!! That VIRTUAL IMAGE from the diverging eyeglass-lens becomes a
new REAL OBJECT (closer!) to the converging eye-lens .. and thus the eye
lens does what it does, and resolves that "close" object as an
image on the back of the eye.
To run the physlet - when it starts, the
eyeglasses are off to the left (away from the "face") - notice
where the light converges .. inside the eye and before it reaches the back
of the eye. Move the eyeglass-lens (the left diverging lens) to the right
... past the "object" and place it where it needs to be so that
the light will converge on the back of the eye. Now look at the light that
comes out of the diverging lens, toward the eye's converging lens ... it
looks like it is coming from a point much closer to the eye than where the
object really is - and, that new "object" point is inside the
far point!! That's why the eye can now see the object "correctly"
.. the diverging eyeglass has tricked the eye into thinking the object is
much closer than it appears!
If necessary, click here to refresh
applet