Why can you see stars (1/r or 1/r^2 dropoff of power)?

[xerxes73]

I read somewhere that people can see stars because an electromagnetic wave drops off by 1/r, therefore the power delivered by the electromagnetic wave stays strong enough to activate the receptors in your eye. I believe, this 1/r relation was realized by Maxwell when he was analyzing and combining the Maxwell equations. But, even still, the intensity or flux of light waves should be dropping off by 1/r^2 because (according to Gauss' law) the light from that distant star all passes through a notional sphere that gets bigger and bigger the farther one gets away from that distant star. The sphere expands by r^2 for an increase of distance r. So why doesn't the intensity of the light drop off by 1/r^2 or does it? Even though the light itself decreases by 1/r, the intensity still has to follow this 1/r^2 relation.

Your eye being triggered depends on the power delivered by that electromagnetic radiation right? If this is true, what would be the equation for this? Dependent on 1/r or 1/r^2?

If someone could just generally shed some illumination on this overall situation and what is going on here with 1/r versus 1/r^2 and when one or the other matters, I would greatly appreciate it. Thanks! -xerxes73

 

[olgranpappy]

I read somewhere that people can see stars because an electromagnetic wave drops off by 1/r, therefore the power delivered by the electromagnetic wave stays strong enough to activate the receptors in your eye. I believe, this 1/r relation was realized by Maxwell when he was analyzing and combining the Maxwell equations. But, even still, the intensity or flux of light waves should be dropping off by 1/r^2 because (according to Gauss' law) the light from that distant star all passes through a notional sphere that gets bigger and bigger the farther one gets away from that distant star. The sphere expands by r^2 for an increase of distance r. So why doesn't the intensity of the light drop off by 1/r^2 or does it? Even though the light itself decreases by 1/r, the intensity still has to follow this 1/r^2 relation.

Your eye being triggered depends on the power delivered by that electromagnetic radiation right? If this is true, what would be the equation for this? Dependent on 1/r or 1/r^2?

If someone could just generally shed some illumination on this overall situation and what is going on here with 1/r versus 1/r^2 and when one or the other matters, I would greatly appreciate it. Thanks! -xerxes73

The intensity is the square of the field. So if the field goes like 1/r the intensity goes like 1/r^2.

This is the case for light radiating from a localized source (like a star); the electric and magnetic fields both depend on the distance from the star as
$$E\sim\frac{1}{r}e^{ikr}\;,$$
where ck is the angular frequency of the light.

As for the intensity:
$$I\sim |E|^2\sim \frac{1}{r^2}\;.$$

 

[astrokreng]

I can provide an explanation for why we can see stars and how the 1/r or 1/r^2 dropoff of power plays a role in this phenomenon. Firstly, the 1/r or 1/r^2 dropoff of power is related to the inverse square law, which states that the intensity of a point source (such as a star) decreases as the square of the distance from the source increases. This means that the farther away we are from a star, the less intense its light will appear to us.

Now, when it comes to seeing stars, it is important to understand that our eyes have receptors called rods and cones that are specifically designed to detect light. These receptors are sensitive to the power of the electromagnetic radiation that reaches them. This means that the intensity of the light reaching our eyes is crucial for us to be able to see stars.

So, why can we still see stars even though the intensity of the light decreases with distance? This is where the 1/r or 1/r^2 dropoff of power comes into play. The 1/r dropoff refers to the decrease in the energy of the electromagnetic radiation as it spreads out over an increasing area. This is why the intensity of the light decreases as we move farther away from the source. However, the 1/r^2 dropoff is related to the decrease in the number of photons (or individual particles of light) reaching our eyes. This is because the photons spread out over a larger area as they travel, leading to a decrease in the number of photons that reach our eyes. This is what causes the decrease in intensity that we observe.

In summary, the 1/r or 1/r^2 dropoff of power is crucial for us to be able to see stars. The 1/r dropoff is responsible for the decrease in intensity of the light, while the 1/r^2 dropoff explains the decrease in the number of photons reaching our eyes. Both of these factors work together to allow us to see stars, even though they are incredibly far away. I hope this explanation helps to shed some light on the situation.