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Old Oct 9th 2013, 08:20 AM   #1
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question about light

I'm interested in this situation:

Let's suppose a lighthouse working for 10 years or so. That is, saturating the immediate environment with photons.

And there's me walking towards the lighthouse, but still miles away. I cannot see the lighthouse. Yet, when I put on my binoculars, I can see the distant light. (Let’s exclude any occultation – for example, let’s say I come by sea).

And here's my question: why?

Why when putting on the binoculars I can see the light from the lighthouse, but otherwise I cannot see it?

Moreover, aren’t those photons everywhere around? Shouldn’t I see a sea of photons?

Many thanks.
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Old Oct 9th 2013, 09:11 AM   #2
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Binoculars act as a sort of "light bucket" (a term fondly used by astronomers to describe what a telescope does). Because the front lens of the binaoculars are larger than the size of the pupils of your eyes, they are able to collect more photons per unit time and direct them through the binnocular's optics to your eye. Thus the source of light (be it a lighthouse or a distant star in the night sky) appears brighter to you. For a source that may be so dim as to be invisible to the naked eye (meaning that too few photons per second are striking your eye for your brain to detect) using binoculars increases the rate of photons hitting your eye and the object can suddenly become visible to you.

Let's put some numbers on it. When looking up at the stars on a very dark night the pupils of an average person's eyes can dilate to about 6 mm diameter. The diameter of typical pair if field binoculars is 50 mm across. This the ratio of area is 50^2/6^2 = 70, which means with binoculars you can see a light source that is 1/70 as bright as you can with the naked eye. Now consider a typical telescope: a popluar size for amateur astronomy uses a 200 mm primary mirror, which means with it you can see objects 1/1111 times as bright as what you can see with the naked eye.

As for why you don't see "a sea of photons" - remember that photons move at the speed of light, so they don't hang around. Photons that were generated by the lighthouse yesterday - or even just 1 second ago - are long gone. What you see are only those photons that happen to hit your eye at the time that you are looking at the lighthouse. All other photons are "wasted" as far as your ability to see the source is concerned. This is the fundamental reason why the brightness of an object obeys the inverse square law - if you double the distance between yuo and the source the number of photons that happen to hit your eye falls off by a factor of 4, and so the object appears to be only 1/4 as bright.

Last edited by ChipB; Oct 9th 2013 at 09:17 AM.
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Old Oct 9th 2013, 10:05 AM   #3
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I have moved neil's post to a new thread. But to ChipB he said:
Thanks for your kind and prompt reply. Moreover, explanatory. In regard to the sea of photons, I donít know what I was thinking: perhaps thatís how I am when tired: stupid (and Iím so tired right now).
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Old Oct 30th 2013, 09:35 PM   #4
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You must know by now your article goes to the nitty-gritty of the subject.
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Old Nov 13th 2013, 10:22 PM   #5
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A Sony camera and a magnifying glass

Hi guys this is my very first chat with anyone about the physics I have loved for many rears now. Further to the photons captured by the naked eye and then the binoculars at the direction of the light house. I once used my magnifying glass to study a small dead insect. And I had at the time a very good sony digital camera. I took a photo through the magnifying glass of the insect with the camera lens at the same distance as my eyes were when range was optimal for enlargement and clarity. However the photo showed no magnification of the insect at all. It was as the magnifying glass was not present.
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Old Nov 14th 2013, 03:54 AM   #6
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The focal length of the camera and that of the eye at that point may have been different causing the images to be different too.
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Old Sep 23rd 2014, 05:35 AM   #7
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Originally Posted by neil View Post
I'm interested in this situation:

Let's suppose a lighthouse working for 10 years or so. That is, saturating the immediate environment with photons.

And there's me walking towards the lighthouse, but still miles away. I cannot see the lighthouse. Yet, when I put on my binoculars, I can see the distant light. (Letís exclude any occultation Ė for example, letís say I come by sea).

And here's my question: why?

Why when putting on the binoculars I can see the light from the lighthouse, but otherwise I cannot see it?

Moreover, arenít those photons everywhere around? Shouldnít I see a sea of photons?

Many thanks.

Neil,

Binoculars have larger diameter compared to your eyes and that brings something else other than explained above: Lower angular resolution, whic is defined as

Angular resolution = (1,22 x wavelength of light) / diameter of the lens

In the case with binoculars you get not only more light but also more precision of the object you are looking at.
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Last edited by orsanyuksek; Sep 25th 2014 at 12:29 AM.
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