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B Why doesn't sunlight have infinite energy?

  1. Mar 11, 2018 #1
    In school we are taught that sunlight contains all different frequencies of light. Also that each frequency has it's own unique wavelength and energy (per photon). So my question is that if there are infinitely many different wavelengths of light (much like infinitely many numbers in an interval) and each wavelength has it's own non-zero energy, how don't all these different and infinitely many energies add up to infinity?
     
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  3. Mar 11, 2018 #2

    sophiecentaur

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    Saying that light has an infinite continuum of wavelengths does not imply that 'each wavelength' has to be present with a finite. amount of energy. In pure Euclidean Geometry a white line can be thought of as consisting of an infinity of points. That doesn't mean that the line would be infinitely bright.
    Say you choose to break the spectrum of red light (at the long wavelength end) up into intervals of 10nm. Each interval could have an energy of, say E. If you then choose to break it up into intervals of 1nm, each of those intervals would have an energy of E/10. The total energy would be the same, however small you make your divisions.
     
  4. Mar 11, 2018 #3

    PeroK

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    If you have a continuous spectrum, the total energy would be like an integral, not a sum. It would be like the finite area under a curve. Even though the curve has a height at an infinite number of points, the area under the curve is finite.
     
  5. Mar 11, 2018 #4

    hilbert2

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    It's much the same as a metal sphere having infinitely many points in it and a nonzero density at all points, but still having a finite mass. This kind of things are studied in integral calculus.
     
  6. Mar 11, 2018 #5

    ZapperZ

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    There's a huge error in physics here.

    Sunlight does NOT "... contains all different frequencies of light..." WE do not have a detection scheme to detect an infinite range of frequencies of light, so how in the world can we claim that such a range exists, and exists for sunlight?

    What you were PROBABLY told was that VISIBLE light contains a range of frequencies. This is distinctly different than claiming that sunlight contains an infinite range of frequencies of light.

    If you have a concrete source that told you this from your school, then you should cite the source. Otherwise, we can only guess that you misunderstood or misinterpret what you were told.

    Zz.
     
  7. Mar 11, 2018 #6

    PeroK

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  8. Mar 11, 2018 #7

    sophiecentaur

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  9. Mar 11, 2018 #8

    PeroK

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    I assume the OP came to PF to find where the misconception was, rather than be flamed for not already knowing the answers.

    I assume he's a school kid, not a PhD student.
     
  10. Mar 11, 2018 #9
  11. Mar 11, 2018 #10

    sophiecentaur

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    And the misconception was dealt with at a simple level in the first few replies. What was in post #2 that "flamed" the OP? The issue of holes and peaks in the spectrum of sunlight was not particularly relevant for the OP. Post #5 was possibly a bit harsh but it was criticising the teaching and not the OP. The same question as in the OP would also apply to the light from a halogen bulb.
     
  12. Mar 11, 2018 #11

    PeroK

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    If you have a very large number of things, you can often model this as a continuous distribution.

    One example is that we can model an object as either a very large number of point particles, or as a continuous mass distribution.

    The Sun's EM spectrum has so many different frequencies that it looks like a continuous spectrum.

    To do this mathematically you need the integral calculus.
     
  13. Mar 11, 2018 #12
    Aha, so it is modelled as a continuous spectum, but it isn't really. Thanks for the replies!
     
  14. Mar 11, 2018 #13

    sophiecentaur

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    Nothing happens to the Sun's spectrum "on the way" to affect the finite amount of Power. Perhaps you are misunderstanding the meaning of the word 'Continuous' in this context. It doesn't mean uniform / flat over an infinite range. It means that a spectrometer with a high resolution would measure nearly the same power in a given wavelength interval, as in the next and the next. There is, of course, a hump in the spectrum of visible sunlight arriving at the atmosphere and, even there, it is not a pure black body spectrum (see this link) and note the visible range. The atmosphere introduces a number of deep nulls (but not in the visible range). But the presence or absence of the atmosphere does nothing to make the power infinite - that is an entirely separate (and more basic) issue.
    The Sun produces a finite amount of EM Power so bear that in mind when you are looking for an answer to your original question. Infinite doesn't come into it. The spectrum curve from MF Radio waves to Gamma Rays has a finite area (i.e total power)
     
  15. Mar 11, 2018 #14

    sophiecentaur

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    Further to this: If you were to look at the power arriving from the Sun (or a lightbulb) in a very narrow range, that power would be constantly varying in a noise like way. In a larger bandwidth / range, the level would measure as constant - averaged out.
     
  16. Mar 11, 2018 #15

    BvU

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    Dear dude, :welcome:

    I watched your thread because I thought it was a good question and I didn't have a simple, clear answer (even with a PhD, that can happen :smile:).

    We are indeed being bombarded by photons that arrive in huge numbers per second on a given area. When we measure a spectrum, we count photons that fall in a small range of wavelengths (the resolution of our spectrometer). The better the resolution, the smaller the number of photons that are detected per unit of time. If (theoretically) we would "increase" the resolution to zero, the counting rate would also go to zero. And that's what offsets the infinity you deducted -- thats's my attempt to explain it in a non-calculus way (don't try this in homework)
     
  17. Mar 12, 2018 #16

    sophiecentaur

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    I don't think the photons actually help in this sort of discussion. The real live 'granularity' of many quantities is not bound to the calculus methods that describe macroscopic relationships. In Calculus, the limit we take is δx→0 and not δx→hf, which is far more specific and arbitrary.
     
  18. Mar 12, 2018 #17

    OmCheeto

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    It did for me.
    I have no idea what this means.

    Anyways, @another_dude 's question reminded me of an old unsolved problem of mine.

    1. The problem statement, all variables and given/known data
    Given that black body radiation yields values at all wavelengths, guesstimate how many 700 nm photons per time period are emitted from a human body.

    constants:
    surface area: 1 m^2 (spherical, of course)
    temp: 310 K
    k_B 1.3806485E-23 J/K Boltzmann constant
    h 6.62607E-34 J⋅s Planck constant
    c 299792458 m/s speed of light
    e 2.71828182845905
    λ 700 nm (the limit of human vision on the red end)​

    2. Relevant equations

    Planck's law broken down into bits, as I was sure I would transcribe something wrong
    a = 2*h*c^2/λ^5
    b = h*c/(λ*k_B * T)
    B_λ(λ,T) = a * 1/(e^b - 1) [power output per (area steradian) @ frequency]
    Photon energy = hc/λ

    3. The attempt at a solution

    Find B_λ(λ,T) at 700 and 701 nm, ie power output at each point

    700 nm --> 1.14e-23 W m-2 sr-1 nm-1
    701 nm --> 1.24e-23 W m-2 sr-1 nm-1

    Average those two values.

    1.19e-23 W m-2 sr-1 nm-1

    multiply by the difference in wavelength, 1 nm, yielding bandwidth power output

    1.19e-23 W m-2 sr-1

    since the subject is 1 m2, power output will be
    1.19e-23 W sr-1

    Determine the energy of photons in that range, ie joules/photon @ 700.5 nm

    Photon energy = hc/λ =
    2.84E-19 joules/photon

    I know a watt second = 1 joule ---> watt = joule/sec
    so
    1.19e-23 W sr-1 =
    1.19e-23 joules sec-1 sr-1

    therefore, since we want photons/second, we rearrange:
    1/2.84e-19 photons/joule * 1.19e-23 joules sec-1 sr-1 = 4.19E-05 photons sec-1 sr-1
    which is a very tiny number, so I took the reciprocal, yielding
    23866 seconds per photon
    which is still too large to recognize, so converted that, and came up with:

    A 1 m2 human @ SOT* will emit a 700 nm photon every 6.6 hours.

    So, in answer to the OP's question: although the line is continuous from 700 to 701 nm, the energy of the individual photons in that range limits the output.
    Which I am sure is also true if one were to do these types of calculations from 700 nm to 56700 nm.
    Which, of course, I did.

    Obligatory graph:

    2018.03.12.black.body.output.of.a.human.body.png

    Output in this range, per my calculations: 163 watts per steradian (for a 1 m2 human)
    Total output: 525 watts

    *SOT = Standard Operating Temperature (98.6°F)
     
  19. Mar 12, 2018 #18

    OmCheeto

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    This is somewhat off, per an online calculator, which said the value was supposed to be: 1.23e-23

    But after looking at the maths involved:oldsurprised:, I decided to ignore it.

    As we plebeians say; "Close enough for government work!"
     
  20. Mar 12, 2018 #19

    sophiecentaur

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    It means that, if you don't like the idea of a continuous function then you can either decide to use photons, which correspond to different amounts of energy for each frequency [hf] ( and the step size - granularity - varies over the spectral range) or you can learn about Calculus which does its thing with intervals (validly) that are infinitesimally small so the actual size of interval is not relevant. As in many cases, using photons gives people the illusion of 'understanding a sort of mechanical model.
    When someone decides that the Maths is too hard for a problem then, very often, it's the actual; problem that's too hard but they think they have got it sussed. That's fine but they should then avoid trying to 'explain' the situation to a third party in over simplified terms.
    It's a bit like thinking you 'understand' football when you remember a football score but you don't know anything about the offside rule. (I don't know the offside rule so I avoid trying to explain that stuff and I cannot remember a single football score I have ever been told.)
     
  21. Mar 12, 2018 #20

    bhobba

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    Ever hear of an integral?

    It's part of analysis that resolves all these kind of queries about apparent infinities such as the famous Zeno's paradox.. The integral of the frequencies being emitted by the sun is finite - not infinite.

    Thanks
    Bill
     
    Last edited: Mar 12, 2018
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