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Huygens principle states that every point on the wave front acts as a source. If it is true, then why can't a single source (let's say a bulb) illuminate a whole big room? Why is it dark after some distance from the bulb? According to him it should continue to infinite. Where am I wrong?

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    $\begingroup$ Each point on the wavefront acts as a source. That doesn't mean it's a source with the same power as the original source (light bulb, in your example). $\endgroup$
    – The Photon
    Aug 9, 2019 at 18:18
  • $\begingroup$ @ThePhoton Sounds like an answer to me $\endgroup$ Aug 10, 2019 at 0:11
  • $\begingroup$ On the topic of the Huygens-principle, I encourage you to read mathpages.com/home/kmath242/kmath242.htm In any case, you should not regard the principle as actually true, it just gives an approximately right answer. $\endgroup$
    – GDGDJKJ
    May 3, 2020 at 17:59

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Every point on a spherical wave front acts as a source of a new spherical wavelet. The tangent surface to all of the wavelets becomes the new wavefront. And this process is repeated using the new wavefront to advance (propagate) the wave.

Note that the wavelets are spherical so their amplitude is reduced inversely to their radius as they propagate (as 1/ct or 1/r). This causes the propagating wavefront's amplitude to be reduced in the same way.

So the spherical wave amplitude becomes lower as it propagates.

Note that if the original wave front was a plane wave there would be no reduction in amplitude as it propagates--the tangent surface is a plane--for why, see www.researchgate.net/publication/316994209 the link is given below. Essentially in a planar wave there is a one to one correspondence of between points of the successive planar tangent surfaces, with spherical surfaces there is not. The correspondence is between successive spherical elemental areas which grow in size as the radius increases.

See for Huygens' Principle in general:

http://farside.ph.utexas.edu/teaching/302l/lectures/node150.html

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/huygen.html

https://www.physlink.com/education/askexperts/ae471.cfm

See my paper for a mathematical derivation:

https://www.researchgate.net/publication/316994209

or the update update

https://www.researchgate.net/publication/340085346

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Why is it dark after some distance from the bulb? According to him it should continue to infinite.

That's a great observation! I must have seen Huygen 100 times and never thought of this.

The basic answer is that Huygen's principle is mostly concerning the phase of the waves, in a way. He's talking about how the wave front propagates. This is what you see in the typical diagram consisting of arcs emanating from a point source.

The amplitude of the wave, which corresponds to the illumination in this case, is a function of its spread. This is actually baked into the principle, although you'd never know that from common explanations or diagrams.

A better illustration would have the arcs grow increasingly light as they move away from the source.

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