Re: virtual images and convex lenses

[Tim Forth <tim_forth@HOTMAIL.COM>]

> From: Bernard Cleyet <anngeorg@pacbell.net>
> Subject: Re: virtual images and convex lenses
> Date: Thu, 03 Jan 2002 20:41:30 -0800
>
> Did John and Robert answer your question?

Maybe.

I'll recap the situation. I am holding a magnifying glass at arms length
from my eye, looking at a lamp that is 10 feet away.  That is, the distance
from eye to magnifying glass is much larger than the focal length of the
magnifying glass, and the distance from lens to the lamp is much, much
larger than the focal length.

I wondered why I didn't see the real image of an upside down lamp just
hanging in space. Instead, it looks to me like I am looking through a window
to an upside down world.

Here's what I think you all were saying: That upside down image in the lens
is in fact a real image. It is in fact hanging in space in front of the
lens, but only looks like it is _in_ the magnifying glass.

After first reading this, I found it hard to believe. It doesn't look like
it is hanging in space, closer to me than the magnifying glass, but you all
seem pretty smart, maybe you all are right. How can I check out this out?

If I were right and the image I see in the magnifying glass is different
than the one projected onto a screen, then it ought to be a different size.
After all, the image in the magnifying glass would be farther away. I look
at both images but I couldn't tell if they were different sizes. Maybe I
could see them at the same time? I put the screen in the spot where the
image of the lamp was in focus and then I slid it down to create a split
screen effect, seeing at the same time both the image projected on the wax
paper and the magnifying glass directly.

Not only were they the same size, but every edge continued off the paper
into the lens with nary a break. My eyes were able to focus on both
simultaneously, further adding credibility to the idea that the upside down
image that appears to be in the magnifying glass is in fact the real image
made by the magnifying glass. Human eyes change focus fast, so I confirmed
the situation with a SLR camera. It could easily focus on both parts of (I
give up) the same image.

====

Not done yet, I tried another experiment. Holding the magnifying glass in my
outstretched hand I moved my thumb so that it was blocking the lamp. I could
still see all around the lamp, but not the lamp itself. On the other hand,
if I put the wax paper back into place, I could see the entire lamp on the
paper. Doing the same split screen effect as above was really errie. As I
moved over the scene, my thumb vanished and the lamp reappeared. Give it a
try. I wonder if I can create a magic trick or Discovery Channel toy out of
this.

I wondered how my thumb, which was close to the lens, could block light to
my eyes but not to the wax paper.  After drawing a ray diagram, I think that
I've figured it out. It is hard to explain in words, but I'll try so that
you all can check my thinking.

I suppose that I can still see the lamp on the wax paper for the same reason
that a lens painted half black doesn't  have half an image. Light from say a
point on the top of the lamp doesn't take just one path to get to the
screen. It travels in a cone covering the entire lens. All those rays are
bent by the lens to come back together at the screen. Although painting the
top half of the lens black blocks some of the light, the light from the
bottom half of the lens still gets through and is still focused on the
screen. So the image is dimmer but still there.

Why, then, would my thumb block the image when I am looking through the
magnifying glass without the screen? I think that a carefully drawn ray
diagram shows the answer. Although light from all parts of the lens are
being converged at the focal plane, it isn't like the rays stop there.  They
keep on going. The rays from above and below my thumb come together at the
focal plane, but they aren't going in the right direction to get into my
eye. They appear on the screen since its diffuses the light into all
directions.  As a side note, this explains why the screen image is so much
dimmer. Not only is some of the light absorbed by the wax paper, but it is
being spread in all directions, including directions that would otherwise
not be able to see through the magnifying glass at all. The direct view can
be seen by a much narrower range of angles, so the light is more
concentrated in those and brighter.

Does this make sense?

Tim Forth





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