Olbers' paradox: why is the night sky dark?

[tris_d]

No, that's not right. The far object appears to have one fourth of the area of the near object, so the sensor receives one fourth as much light from it than from the near object. The two objects appear to be the same brightness because the ratio of light being received by the sensor from the object to the apparent size of the object is constant regardless of distance (ignoring the normally negligible light loss due to contaminants in the air etc).

If what you are saying were true, mountains would look black far away, or blindingly bright up close. That is obviously not the case.

I'm not saying anything, yet. That was a question. -- I don't think inverse square law is about apparent size, but about drop of intensity, like this:

Also, TCampbell seems to have agreed that my picture is basically correct. So what now, which is it?

I do not want to talk about stars until we sort out the basics first.

Besides, this part of the experiment is easy enough to test by yourself. Use fixed settings in your camera and take several shots of a constantly-lit object or light source, varying only the distance between your camera and subject. It would probably be best to move the camera rather than the subject to avoid inadvertently changing the lighting conditions.

I would, but I'm not photographer, I do not have a camera where I can set exposure time and aperture size manually. Could you perhaps snap such photo for us?

 

[amolitor]

I think that you have the inverse square law right arithmetically, but I think you have the wrong pictures.

When the stars are twice as far away, they appear 1/4 as bright. You can represent this as a circle the SAME SIZE and 1/4 the brightness, OR as a circle of the SAME brightness with 1/4 the area (1/2 the diameter). You are shrinking the diameters of the circles, and simultaneously dimming them. This is wrong.

In reality, stars are pretty much points. The "image" of a star on any sensor is much much much much smaller than a pixel, or whatever the smallest sensor element it, so we represent it as a single pixel of suitable brightness. In reality, however, a star that is farther away appears less bright because the almost infinitesimal image circle is smaller, not because the brightness of the interior of the circle is any less (assuming that there's nothing in the way).

Olber's paradox hasn't been an issue for quite a while, so I am a little puzzled as to your interest in solving it.

 

[fjrabon]

Yes, if your primary question is 'are my images a correct representation of what happens to stars as they get further away' the answer is no. You can make them smaller, or dimmer as a representation, but not both simultaneously.

 

[tris_d]

Yes, if your primary question is 'are my images a correct representation of what happens to stars as they get further away' the answer is no. You can make them smaller, or dimmer as a representation, but not both simultaneously.

I'm talking about photographing two light bulbs simultaneously, not "making" anything up. It is important the first bulb does not over expose the pixels, so that we can observe the difference in brightness compared to the further light bulb, if any. -- So you say both light bulbs would produce pixels of equal brightness, like this:

That does look more "natural", but I don't think that's how inverse square law is supposed to work. Intensity is supposed to drop with the distance, like on the picture below, and until we have an actual photograph to prove it one way or the other I'd like to wait and see what TCampbell and other people will say.

 

[christop]

Besides, this part of the experiment is easy enough to test by yourself. Use fixed settings in your camera and take several shots of a constantly-lit object or light source, varying only the distance between your camera and subject. It would probably be best to move the camera rather than the subject to avoid inadvertently changing the lighting conditions.

I would, but I'm not photographer, I do not have a camera where I can set exposure time and aperture size manually. Could you perhaps snap such photo for us?

Well, in that case you can do the experiment without a camera. You can do this physically or as a thought experiment based on past experience. Look at an object (say, a ball) at 1 meter from your eye (about an arm's length away). Then throw it to 50 meters (about 164 feet) away. Does it look 2500 times less bright (or 2500 times dimmer, basically black) when it's far away? The same concept applies to stars.

I also think it's a bit... peculiar that you're on a photography forum but you're not a photographer (not that there's anything wrong with that). And while this question is vaguely related to photography, it would better suited to an astronomy forum.

 

[Buckster]

Besides, this part of the experiment is easy enough to test by yourself. Use fixed settings in your camera and take several shots of a constantly-lit object or light source, varying only the distance between your camera and subject. It would probably be best to move the camera rather than the subject to avoid inadvertently changing the lighting conditions.

I would, but I'm not photographer, I do not have a camera where I can set exposure time and aperture size manually. Could you perhaps snap such photo for us?

Well, in that case you can do the experiment without a camera. You can do this physically or as a thought experiment based on past experience. Look at an object (say, a ball) at 1 meter from your eye (about an arm's length away). Then throw it to 50 meters (about 164 feet) away. Does it look 2500 times less bright (or 2500 times dimmer, basically black) when it's far away? The same concept applies to stars.

I also think it's a bit... peculiar that you're on a photography forum but you're not a photographer (not that there's anything wrong with that). And while this question is vaguely related to photography, it would better suited to an astronomy forum.

Or a physics forum.

 

[amolitor]

Yes, if your primary question is 'are my images a correct representation of what happens to stars as they get further away' the answer is no. You can make them smaller, or dimmer as a representation, but not both simultaneously.

I'm talking about photographing two light bulbs simultaneously, not "making" anything up. It is important the first bulb does not over expose the pixels, so that we can observe the difference in brightness compared to the further light bulb, if any. -- So you say both light bulbs would produce pixels of equal brightness, like this:

That does look more "natural", but I don't think that's how inverse square law is supposed to work. Intensity is supposed to drop with the distance, like on the picture below, and until we have an actual photograph to prove it one way or the other I'd like to wait and see what TCampbell and other people will say.

Intensity does drop, but because the light-emitting circle is smaller not because it's dimmer. The picture here is correct.

We don't need even to look at a picture. The correct exposure for any sunlit object is (roughly) given by the sunny-16 rule. This applies to an apple six inches from the lens, as well as to the moon.

This isn't a thing we're voting on, it's physics. It doesn't care what your opinion, or what TCampbell's opinion is.

 

[tris_d]

I think that you have the inverse square law right arithmetically, but I think you have the wrong pictures.

When the stars are twice as far away, they appear 1/4 as bright. You can represent this as a circle the SAME SIZE and 1/4 the brightness, OR as a circle of the SAME brightness with 1/4 the area (1/2 the diameter). You are shrinking the diameters of the circles, and simultaneously dimming them. This is wrong.

In reality, stars are pretty much points. The "image" of a star on any sensor is much much much much smaller than a pixel, or whatever the smallest sensor element it, so we represent it as a single pixel of suitable brightness. In reality, however, a star that is farther away appears less bright because the almost infinitesimal image circle is smaller, not because the brightness of the interior of the circle is any less (assuming that there's nothing in the way).

Olber's paradox hasn't been an issue for quite a while, so I am a little puzzled as to your interest in solving it.

Are you saying as long as they are bigger than one pixel they will keep the brightness and shrink in apparent size, but when they get smaller than one pixel they will start turning to darker shades with the distance?

 

[amolitor]

I also think it's a bit... peculiar that you're on a photography forum but you're not a photographer (not that there's anything wrong with that). And while this question is vaguely related to photography, it would better suited to an astronomy forum.

Oh, I think the OP made it pretty clear that this has been tried out in science forums, and been told to buzz off and go learn some basic stuff.

 

[amolitor]

Are you saying as long as they are bigger than one pixel they will keep the brightness and shrink in apparent size, but when they get smaller than one pixel they will start turning to darker shades with the distance?

Um. When you're dealing with a real sensor, that is in fact what will happen. If you were, for instance, to fly away from the sun, taking photographs of the sun at some specific exposure, the pixel values within the circle of the sun would remain more or less constant (the sun boils around a bit, there might be junk/dust/gas in the way etc, so let's not say EXACTLY constant) until the sun got smaller than the pixel size, at which point that one single pixel's value would start to drop, until it hit zero.

 

[tris_d]

Or a physics forum.

Would you mind snapping a photo of two light bulbs where one is at double the distance than the other? Anyone? -- It is important pixels do not get overexposed, that is photo should not contain any pixel with brightness higher than 99, where 100 is maximum brightness (complete white).

 

[christop]

Or a physics forum.

True.

Astronomy combines a few different scientific disciplines like physics and geometry. I'm kind of a physics nerd, which is probably what attracts me to astronomy and photography.

We don't need even to look at a picture. The correct exposure for any sunlit object is (roughly) given by the sunny-16 rule. This applies to an apple six inches from the lens, as well as to the moon.

That would really suck for us if we had to take subject distance into account when calculating the proper exposure. We'd have to increase the exposure for the moon (356700 km) by 57 stops compared to a sun-lit subject at 1 meter away!

 

[TCampbell]

The light bulbs are the same, further one is at double the distance. And so I take it you confirm my image representing such two light bulbs is correct and the further light bulb would indeed appear dark gray. Ok? -- Now, before I get into argument about stars and the universe, I would like to clear this conclusion a bit more. Consider the photo below, those lights do not seem to shift their brightens to more darker shades with the distance like on my picture, they actually seem to keep their brightness and only shrink in size. Is this because the pixels get over exposed, and if we change exposure time we would actually see those lights do indeed become dimmer (darker shades) as my image would suggets?

There are more rules involved. The nearest light does appear brighter than the next light. The next light appears to be much smaller even though we know they're really the same size.

Also, stars are so distant that they all resolve to a pinpoint even in the largest scopes (well.. they resolve to an "Airy disk" due to the wave nature of light. We would have to magnify a point of light considerably to see it that way and it really only works on stars because they're the point sources of light that are so far away that they really do appear to be a "point" and not a larger surface area.) That means that if we use actual stars instead of street lights, they'll basically appear to be the same size... but different brightnesses. They wont appear to be both bigger AND bright as you've depicted in your diagram. They're all far enough away that none of them appear to have a large physical diameter as you have in this photo of streetlights.

However... if we use a light meter to measure the light, we could report the distance to each of these street lights with a fair degree of accuracy as long as we know the baseline distance to at least one light and if the lights are all equally bright.

What exactly is your question?

Are you asking if the inverse-square law works? Yes.

Are you asking why Olbers' paradox breaks down? It breaks down because it is based on several incorrect assumptions, over-simplifies rules, and then ignores a few other realities of the physical universe.

 

[tris_d]

Are you saying as long as they are bigger than one pixel they will keep the brightness and shrink in apparent size, but when they get smaller than one pixel they will start turning to darker shades with the distance?

Um. When you're dealing with a real sensor, that is in fact what will happen. If you were, for instance, to fly away from the sun, taking photographs of the sun at some specific exposure, the pixel values within the circle of the sun would remain more or less constant (the sun boils around a bit, there might be junk/dust/gas in the way etc, so let's not say EXACTLY constant) until the sun got smaller than the pixel size, at which point that one single pixel's value would start to drop, until it hit zero.

Ok. That sounds reasonable enough, but again, that's not what this picture below would suggest, is it?

 

[amolitor]

Ok. That sounds reasonable enough, but again, that's not what this picture below would suggest, is it?

The picture is actually pretty miserable, since it suggests a "focused" light that's NOT falling off as the inverse square. Lasers do not follow the inverse square law, and I think to a less extent spotlights do not either, and this picture looks a little spotlight-ish.

Still, the numerical values give for falloff are fine, I think.

The total amount of light does fall off as indicated. In our "flying away from the sun" scenario, when you get 8x as far from the sun as when you started, there will only be 1/64 as many pixels inside the image circle of the sun on the sensor, so there's 1/64 as much total light falling on the sensor. In fact, since we KNOW the circle of pixels is 1/8th the diameter (this is simple geometry), we then KNOW that there are only 1/64 as many pixels in it (again, simple geometry). Since we also know, from the inverse square law, that the total light is down by 1/64, we KNOW that each pixel MUST be just as bright as it was originally. Otherwise there would be missing light.