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I am told that one of the merits of Huygens' principle is that it could explain refraction, however, in the argument given in my textbook it seems flawed.

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This seems like a totally idealised scenario because if I wait a little bit longer,

enter image description here

(If drawn more accurately, the wave fronts shown in the refraction would line up with the wavelets all the time, I don't believe this would be a problem) with the same reasoning, I can assert that the wavefronts are travelling in an entirely different direction. Is this really the correct justification for refraction given with Huygen's theory?

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    $\begingroup$ consider time evolution. The wavefronts you should join are like a picture at a given time. You are joining wavefronts from secondary emitters which do not correspond to a given $t=t_0.$ So for example, join the first wave fronts that each of the secondary emitters have produced. Then join the second ones and so on. It would look like the book's. $\endgroup$ – Nelson Vanegas A. May 4 '20 at 20:02
  • $\begingroup$ This is probably a homework problem? $\endgroup$ – user262759 May 4 '20 at 23:50
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In order to build the "new" wavefront from the spherical secondary wavefronts, you must connect only the ones that belonged to same wavefront before entering the slower medium, that is the ones that have walked the same number of wavelengths.

For example, in the picture from your textbook there are 5 white spaces, that is 5 wavelengths, between the first line (let us consider it our source) and both points A and C: then A and C belong to the same wavefront.

Same thing holds for points B and D: the point B has travelled 10 wavelengths in the old medium, while the point D has travelled 5 wavelengths in the 1st medium + 5 in the 2nd one.

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