Re: Why does refllection off of a glass window change with distance from window

Hi, Eric!

I don't know the specifics of your window (how many panes, what kind of 
coatings, etc.), or, the lighting of the room you are in. Also, I'm kind of 
writing in "hurry-up" mode, as I've already taken far too long answering 
your question. Nevertheless, I think I know what you are talking about, so 
here goes…

Reflection of light from window glass is a tricky thing. It depends upon 
your viewing angle, the angle of light coming from the (inside) source, the 
intensity and spectrum of the light both inside and outside, and a whole 
bunch of other factors like coatings, layers of glass, etc.

Imagine you are standing in a room lit by a single lamp-bulb. Let's say 
that bulb is equidistant between you and the window, maybe off to your 
right side by a few feet, so we have a nice triangle between you, the lamp, 
and the window. (Try drawing this as a view from above.) Some light rays 
leave the bulb and bounce off the window back into the room. An equal 
number might leave the bulb, bounce off you, and go out the window. Some of 
these rays (plus the ones reflected off the window, back to you, then back 
to the window) never make it out the window, but get reflected back to your 
eye, which "gobbles them up" and creates the image you see.

Let's further assume that about 95% of the light hitting the window goes 
straight through to the outside. That would mean only about 5% of the light 
hitting the window from the inside can actually be reflected back into your 
eye. (Those figures aren't exact. Like I said, there are lots of 
complicated factors involved here. 5% is a pretty good "ballpark" figure to 
start with, though.)

Now, let's say you take a few steps toward the window, so that you are in 
line with the lamp, but still right in front of the window. Fewer light 
beams leave the bulb, bounce off you, and get reflected from the window. 
Why? Remember the triangle I mentioned before? One corner represented the 
window, one the bulb, and one you. If you draw this triangle, then move the 
"you" corner towards the window corner so that it stops in line with the 
"lamp", half our triangle has disappeared. This is important, because we 
often think of light "rays" as straight lines. If you draw a whole bunch of 
lines from the "lamp" corner to where "you" started, and keep drawing lines 
until you hit the new "you" (moved halfway towards the window), you will 
color in half your original triangle. Think of these as light rays which 
"can't" hit you any more, but have to bounce off something else in the 
room. Less light bounces directly off you and goes to the window, so, less 
light can be reflected back to your eye.

Let's "cheat" and say only half the light hitting you before you walked 
toward the window is hitting you now that you are halfway there. If you 
were in a room with one bare bulb and nothing but black curtains for walls, 
this might be about the case. (I'm simplifying the math, here. The 
important thing is: the light which did not hit you would be absorbed by 
the curtains, never to be seen again.) You might find you could only see 
half your face in the reflection, because the other side would be away from 
the bulb, therefore, in shadow.

You started off seeing 5% of the TOTAL light inside the room reflected off 
the glass. You've just cut that down to 2.5% (half) by moving towards the 
window. Now, let's say the light coming from outside is only 2% the 
intensity of the TOTAL light inside the room. The amount of light 
reflecting from inside the room is getting very close to that coming from 
outside the room…the intensity of light reflected off you is nearing that 
which comes from outside the window.

By getting closer to the window you are cutting down the angle of light 
which can reflect off you and to the window. Take another step…then 
another. Fewer and fewer light rays can bounce directly off the bulb, hit 
you, then be reflected off the window into your eye. 

Neither the outside, nor, the inside light changes one bit. The light rays 
and reflections are still there. You've just changed your viewing angle, 
and, therefore, the relative amount of  each "kind" of light hitting your 
eye. 

There are a couple of other ways you can demonstrate this for yourself. 
First, try taking a flashlight into a totally dark bathroom. Shine it 
directly on your face and look at your reflection in the bathroom mirror. 
Now, shine the light straight up from under your chin. Less light bounces 
off your face and into the mirror, so you see some really cool, spooky, 
"dark shadows" on your face.

Another thing you could try is looking in a car's rearview mirror at night. 
Most of these mirrors have a  switch setting for day, and for night. All 
this does is tilt the mirror by about 5 degrees…you can feel it change with 
your hands. That's enough to make sure you only see the small percentage of 
light which bounces off the surface of the glass, instead of the other 95% 
of the light which would normally bounce off the mirrored back surface of 
the glass. (It would probably be good to have someone else do the driving 
for this experiment. You also don't want to do this in heavy traffic, as 
your driver will probably need to use their rearview mirror to keep from 
hitting people. Make sure to ask your driver politely in advance, because 
safety on the road is ALWAYS much more important than this experiment! 
Maybe if you were at a stop light? ;)

I've only been able to explain a little bit about this, Eric. There's so 
much more to know! Just thinking about this question could lead you to 
investigate: reflection, refraction, basic optics & physics, scattering, 
the nature of light and the way humans perceive it, the human eye, 
different kinds of math like trigonometry and calculus, quantum theory…and 
a whole bunch of other stuff! (That's why this is such a good question. It 
makes you think. If you think you don't know the answer to a question, then 
you might have to learn some stuff to get your answer…which leads to 
understanding of a lot of things you didn't even think about in the first 
place! Ask one good question and, "boom"! You're a genius!)

If you would like more details / references, or, if I've been unclear (or, 
wrong), please feel free to e-mail me at mwnet@swbell.net. I not only like 
your question because it teaches us all something, but because I always 
wondered about the same thing myself when I looked out the window on an 
overcast afternoon. I'd be happy to help with some more research on this 
great mystery of the universe!

Your friend & MadSci,
-Matt
mwnet@swbell.net
mweyeric@cpicorp.com