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This may be a ridiculous question, but I'll learn something from it! Let's say there's a TV transmitter transmitting at 100kW. I can receive the station just fine 20 miles away. The antenna is 300m in the air. If I replicate this but with light (put a 100kW "bulb" 300m in the air), would I be able to see the light 20 miles away?

I understand there are things to take into account, particularly propagation differences at the different frequencies. But is this a meaningful analogy, or totally useless?

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    $\begingroup$ I'll just add something: to be precise, if you call the radiation produced by a light bulb by "light", then the radiation your antenna gives off is also called "light"... The difference is that the light bulb's is visible, but they're both light. $\endgroup$ – QuantumBrick Sep 3 '16 at 0:52
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    $\begingroup$ Is your question about whether your eyes would be able to detect the light? In other words, comparing the sensitivity of your eyes and the receiver in the TV? Or are you just asking whether both frequencies take the same path? In the second case, I think that the frequencies can make a difference. Very long wavelengths (low frequencies) can bend around the earth. A LW station, e.g. BBC Radio 4 in the UK at 198kHz, can be received very far away from its transmitter. Much further than the higher frequency FM broadcasts at about 93MHz. $\endgroup$ – badjohn Aug 15 '17 at 14:45
  • $\begingroup$ Some information here en.wikipedia.org/wiki/Radio_wave, see Ground waves. However, this seems to be only significant at very low frequencies e.g. medium wave and long wave. I don't think that the effect is significant at the frequencies normally used for TV signals. For example, I mentioned BBC Radio 4. It has a single LW transmitter in Droitwich (central England) but I have received it in Germany. The FM service requires multiple transmitters just to cover the UK, $\endgroup$ – badjohn Aug 15 '17 at 14:52
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Technically speaking, if there is no decay of EM waves of any particular frequency, you can measure the signal in the configuration you are describing. It all depends on how sensitive the measuring instrument (antenna, eye) is to the power under consideration. This of course being true for some large values of EM wave intensity where quantum effects would be irrelevant.

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100 watts is 1600 lumens. The problem now is how many lumens does 1 candle put out. Yes, these are very old fashioned units.

Estimates vary as to what the equivalence is, but I have settled for the most quoted figure.

A standard candle is defined as giving off one candlepower over $4 ×\pi$ steradians, this comes to 12.56636 lumens.

So a 100 watt bulb should give out the same light as 127 candles.

From Comparing Candle to Stars, based on work done by researchers testing how dim a light you could expect to see, by comparing a candle at a distance to a star of known magnitude.

The brightest stars, such as Vega, have a magnitude 0. At what distance would a candle flame be comparable to a star like Vega. Some straightforward nighttime experiments with a candle suggested that the distance was 338 meters. “To our eyes the candle flame and Vega appeared of comparable brightness,” they say.

To check, the team observed both Vega and the candle flame using the same digital camera (an astronomical SBIG camera with 35mm aperture and 100mm focal length).The results were something of a surprise. “The candle flame at 338 m was 2.423 magnitudes brighter than Vega, even though they looked comparable in brightness to our eyes,” say Krisciunas and Carona.

That raises the question of how far away the flame should be to appear the same brightness as Vega. That’s not a straightforward question to answer because the camera’s CCD is sensitive to photons in a different way to human eyes and Vega and the candle emit light with different spectra. Nevertheless, Krisciunas and Carona make some calibrating assumptions and say that parity would occur at 392 meters. In other words, a candle flame is the same brightness as a magnitude 0 star at a distance of 392 meters.

The faintest stars humans can see unaided have a magnitude 6. Fainter stars can only be seen using a telescope or binoculars. Magnitude 0 stars are 251.2 times brighter than magnitude 6 stars. So while again taking into account the differences between starlight and candle light, it is possible to work out how far away the candle should be to appear equally bright as a magnitude 6 star.

Krisciunas and Carona say this would occur at a distance of 2,576 meters or roughly 1.6 miles, and that at 10 miles a candle would appear as bright as a magnitude 9.98 star. “This is far beyond the capabilities of the most sensitive human eyes,” they say.

So the farthest distance a human eye can detect a candle flame is 2.76 kilometers. From 10 miles a candle would appear as bright as a magnitude 9.98 star. “This is far beyond the capabilities of the most sensitive human eyes,” they say.

Now the magnitude of stars goes like this.

From Magnitude of Stars

Thus in 1856 Norman Pogson of Oxford proposed that a logarithmic scale of ${\displaystyle {\sqrt[{5}]{100}}\approx }$ 2.512 be adopted between magnitudes, so five magnitude steps corresponded precisely to a factor of 100 in brightness. Every interval of one magnitude equates to a variation in brightness of 1001/5 or roughly 2.512 times. Consequently, a first magnitude star is about 2.5 times brighter than a second magnitude star, 2.52 brighter than a third magnitude star, 2.53 brighter than a fourth magnitude star, and so on.

Now you have 127 candles, so no, you should not be able to see it. They just won't bring it down to magnitude 6, the minimum brightness requipped to see it.

This assumes pitch blackness, like a star in a clear sky.

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