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In The Fundamental of Optics 4th edition by F Jenkins,H white there is a paragraph -"Huygens' supposed the secondary waves to be effective only at the point of tangency to their common envelope ,thus denying the possibility of diffraction.The correct application of the principle was first made by Fresnel."

I can not understand why huygens' principle did not explain diffraction.

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  • $\begingroup$ because the diffracted waves do not propagate backwards while the simple Huygens spherical wavelets do $\endgroup$ – hyportnex Jun 23 '17 at 12:35
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    $\begingroup$ The last sentence "The correct application of the principle was first made by Fresnel" means Huygens principle does explain diffraction if applied correctly. I don't understand the question. $\endgroup$ – Mo_ Jun 23 '17 at 12:53
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In the original statement of the principle by Huygens (sometimes known as the Huygens principle of wave propagation), he stated that every point on the propagating wavefront serves as a secondary spherical source, which together add up and build the wavefront in some distance ahead, but only those points of the secondary spherical waves count that are tangent to the wavefront #2. (figure below)

One of the consequences of this limitation is that in a diffractive setup like an aperture, light will not propagate in the geometrical shadow zone (as depicted in the figure) because no fictitous source on the wavefront #1 has a wavefron tanget to those points of wavefront #2 that are located in the geometrical shadow region.

                              enter image description here

Fresnel expanded this principle by adding a couple of multiplicative factors to the secondary spherical waves, and removing the restriction above. As stated in this answer, the observed field at a secondary wavefront is a sum of diverging spherical waves in the form of $\dfrac{\exp{(jkr})}{r}$ located at each and every point in the aperture (as stated in the original Huygens principle), multiplied by a factor of $\dfrac{1}{j\lambda}\,U_I(x',y') \cos \theta$. This modification makes the principle fully consistent with the Rayleigh-Sommerfeld formula for scalar diffraction, obtained from the Maxwell's equations.

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