If a torch is switched on and pointed towards the moon, would the light from the torch reach to the moon?
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$\begingroup$ in theory, light from a flashlight (torch) will eventually reach all parts of our visible universe, though it will become extremely faint with distance. People have bounced lasers off the moon, but a regular flashlight might disperse light too much. $\endgroup$– user21Jul 15, 2017 at 0:37
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1$\begingroup$ Related XKCD: what-if.xkcd.com/13 $\endgroup$– userLTKJul 15, 2017 at 3:25
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$\begingroup$ @barrycarter you're misusing "disperse" there. Better to say "beam spread" to indicate that most of the photons from a flashlight will miss the moon entirely. $\endgroup$– Carl WitthoftJul 17, 2017 at 12:40
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$\begingroup$ "distribute or spread over a wide area" is the definition of disperse and it seems appropriate. But, yes, the "wide area" I meant is much wider than the moon. $\endgroup$– user21Jul 17, 2017 at 13:09
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1$\begingroup$ @barrycarter but that is not the definition within the field of optics, and of astronomy. $\endgroup$– Carl WitthoftJul 17, 2017 at 18:56
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2 Answers
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Visible light from a torch has a 50% (blue light) to 90% (red light) chance of making it through the Earth's atmosphere, depending on the amount of dust and aerosols in the atmosphere and how close the Moon is to the horizon.
Light travels in straight lines. The Moon has an angular diameter of only 0.5 degrees as seen from the Earth. Most ordinary torch beams diverge by much more than this, so only a small fraction of the photons from a torch would pass through a circle of angular diameter 0.5 degrees. Hence only a small fraction of the emitted photons would hit the Moon.
Finally, you said that the torch was pointed "towards the Moon". Actually, you pointed it to where the Moon was 1.5 seconds ago, and the torch light reaches the distance of the Moon a further 1.5 seconds later. Thus the Moon has travelled 3 seconds in its orbit. However, since the orbital period (360 degrees) is a month, then it only covers an angle of 1.5 arcseconds in 3 seconds, so this shift is not relevant for your experiment (though it is for those bouncing lasers off reflectors on the Moon, which proves that light does in fact reach the Moon).
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Yes. If there is nothing opaque in the way to obstruct it, it will reach the moon. However, the intensity of light (from a point source like a torch) diminishes with the square of distance. So, by the time it reaches the moon, it will be extremely faint.
Further information on the inverse square law as applied to light from a point source: https://en.wikipedia.org/wiki/Inverse-square_law#Light_and_other_electromagnetic_radiation
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$\begingroup$ A torch, aka flashlight,is not a point source, nor is it uncollimated. $\endgroup$ Jul 17, 2017 at 12:39
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$\begingroup$ A flashlight can be treated as point light source, but I agree it's not collimated (though neither is it omnidirectional) $\endgroup$– user21Jul 17, 2017 at 13:11
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$\begingroup$ @barrycarter you misread my comment. A torch is partially collimated by way of the parabolic reflector behind the bulb. $\endgroup$ Jul 17, 2017 at 18:57
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$\begingroup$ For the distances in question, light from a torch approximates a point source quite reasonably. That is, however, a side point to the answer. The question is whether photons from a torch reach the moon, and the answer is that they do unless something gets in the way. The intensity only really becomes a factor in the follow-up question "Could we see it?". $\endgroup$– hartacusJul 18, 2017 at 3:30
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$\begingroup$ If we had a "perfect" laser, the intensity wouldn't decrease either. The 1/(r^2) rule only applies because the light spreads out over a larger area. A "perfect" laser would mean all the "photons" arrive intact. $\endgroup$– user21Jul 18, 2017 at 3:36