Really stupid physics question

[fjrabon]

Take a piece of paper and put lit candle 10cm away from it, you see a bright blob on the paper. Move the candle to 20cm away from the paper and you see not only four times smaller blob, but is also four times less bright. Correct?

Actually, incorrect.

haha, actually in his example the blob gets bigger, not smaller. Like hes seriously never flashed a flashlight at a sheet?

 

[unpopular]

He's probably a physics grad student at Cornell just trying to **** with us.

Physicist troll....

 

[Helen B]

All I see is they told you, like they told me, that things appear four times smaller at double the distance and that is supposed to explain inverse square law, which it does not.

You are precisely and exactly wrong, here. Lest someone stumble across this and become confused, let me be quite clear: Tris is wrong on this point. Things appear 4 times smaller at double the distance, and that is exactly the explanation for the inverse square law.

Just please point some reference. Surely if what you say is true it should be mentioned in some text books, there would be some article on the internet about it, right? It's not some kind of secret knowledge, I suppose, so please just give me some link where I can confirm what you are saying.

It is mentioned in many textbooks, and in many places on the internet, but I guess that you can't recognize it for what it is. Here's one version from Optics in Photography by Rudolf Kingslake, who used to be the Director of Optical Design at Eastman Kodak, and Emeritus Professor at the University of Rochester. He also received the Gold Medal from The International Society for Optical Engineering. I don't think he has a blog, or even a Facebook page, so I'm not sure if he can really be trusted, to be honest.

E = t π B / (4 N^2)

Where
E is the image illumination,
t is the lens transmittance (dimensionless),
π is Pi (dimensionless),
B is the object brightness (at the object), and
N is the f-number (dimensionless).

Note the absence of any term relating to the distance to the object.

 

[tris_d]

NO!!

Because the blob becomes smaller at the same rate which the energy is dispersed, the blob's relative intensity stays the same.

Light has intensity, blob has brightness. I'm talking about blob's brightness.

Previously you said:
- "What that light illuminates does not focus it, this is why inverse square appears to apply to ambient illumination.."

Brightness is determined by energy distribution, not quantity.

But quantity is determined by distribution. That's what inverse square law is about. Distribution gets more sparse and thus quantity per surface area becomes less. Less dense distribution means less quantity, which means less brightness.

See Lumen (unit) - Wikipedia, the free encyclopedia and by extension Lux - Wikipedia, the free encyclopedia

and for god sake, follow every single link that you don't understand.

What exactly should I look at there, what parts are you referring to?

 

[unpopular]

helen's equation is more concise.

but seriously, if you can't get this from what has been said, you have a LONG ways to go.

 

[tris_d]

haha, actually in his example the blob gets bigger, not smaller. Like hes seriously never flashed a flashlight at a sheet?

You are right. I was thinking of the blob I get as a reflection on my LCD.

 

[christop]

I don't think he has a blog, or even a Facebook page, so I'm not sure if he can really be trusted, to be honest.

Lol.

 

[fjrabon]

here's my last try:

I got PICTURES!

First, to sort of disprove your idea earlier of the blob getting smaller and dimmer:

First a piece of paper resting on a lamp, with none of the image clipped:


DSC_4405 by franklinrabon, on Flickr

Next, picked off of the lamp by 1/4"


DSC_4406 by franklinrabon, on Flickr

Finally about an inch above the lamp:


DSC_4407 by franklinrabon, on Flickr

As you can see, the 'blob' gets bigger, as the light gets dimmer.

What this doesn't mean was that if I was to look at the lamp directly that the actual lamp itself would appear dimmer. It's that the total light falling on my eye would be less, because it's coming from a smaller part of my visual frame, due to how our eyes focus. Once you take focus out of the equation, further light sources are actually in some sense bigger the further they are.

here is a sort of graphical explanation with some writing and diagrams as well:


DSC_4404 by franklinrabon, on Flickr

 

[tris_d]

Why? Because Physics said so, that's why!

What physics, what equation? Where did you read about it? Can you point some reference? Where exactly is the difference between a paper and a photo?

maybe you should start with Pythagorean Theorem.

If you don't know how that applies, then maybe you should start here:

Lens (optics) - Wikipedia, the free encyclopedia

Where exactly is the difference between a paper and a photo?

 

[unpopular]

the lack of a lens in front of the paper.

 

[tris_d]

Your issue is this, which we have said multiple times: THE INVERSE SQUARE LAW ONLY APPLIES TO POINT SOURCES, ie sources of light that do not have any dimensionality and radiate light equally from that point in all directions. You can then generalize that to other forms, based on a serious of more complicated equations, or just fudge it, if the non point object is small enough.

Finally we can agree on something, so let's take it from here. Consider what Isaac said:
- "If you have a spherical light source (like one of those oriental paper lanterns), it still follows the inverse square law no matter how close you are to it. You can think of this as a quirk peculiar to spheres."


Does what he said not mean if we photograph such spherical light source it will produce less bright blob on the image proportionally to the square of the distance, as if it was a point light source?

 

[fjrabon]

Your issue is this, which we have said multiple times: THE INVERSE SQUARE LAW ONLY APPLIES TO POINT SOURCES, ie sources of light that do not have any dimensionality and radiate light equally from that point in all directions. You can then generalize that to other forms, based on a serious of more complicated equations, or just fudge it, if the non point object is small enough.

Finally we can agree on something, so let's take it from here. Consider what Isaac said:
- "If you have a spherical light source (like one of those oriental paper lanterns), it still follows the inverse square law no matter how close you are to it. You can think of this as a quirk peculiar to spheres."


Does what he said not mean if we photograph such spherical light source it will produce less bright blob on the image proportionally to the square of the distance, as if it was a point light source?

No, because you're optically altering the light due to having a lens in front of it. You're taking all that dispersed light and then recombining it into a smaller light, of equal brightness. Which is why we kept telling you all along that you can represent the falloff as the light sources being dimmer, or smaller, BUT NOT BOTH.

 

[Bitter Jeweler]

 

[christop]

Think about this....

You have two identical pieces of paper, one at 1m and the other at 2m from a spherical light source (such as a paper lantern). The paper at 2m receives one fourth as much light as the paper at 1m, so it appears dimmer. Correct?

Ok, so now we replace the square papers with square lenses of the same size. The total amount of light energy that passes through the lenses is the same as was originally illuminating the papers. We then put a flat surface behind the lenses so we can view the real image of the light sphere that is projected by each lens. The surfaces are placed at the same distance behind each lens. This surface could be a sensor or film if we wish to record the image.

The lens at 2m projects an image onto the surface that is half the size (one quarter of the area) as the lens at 1m. Since the total amount of light projected into that image is also one quarter as much as the image at 1m, the image appears just as bright on both images.

 

[fjrabon]

FInally, I was able to find a lamp that gave reasonable exposures and could do your 'test' from earlier:

lamp, 1 ft away


DSC_4410 by franklinrabon, on Flickr

Lamp, 2 ft away


DSC_4411 by franklinrabon, on Flickr

In the first image, does the lamp look 4 times brighter? It makes up a small enough portion of the visual frame that the inverse square law would only be off by about 5%. So I guess you'd be asking does it look 395% brighter, technically.