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?
Answer
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 for a mathematical derivation:
https://www.researchgate.net/publication/316994209
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