# Diffraction according to Huygens principle - struggling with the concept of diffraction being caused by small point source wavelets

Huygen's principle states that every plane wave is made up of an infinite number of point sources, and that the constructive interference between each wavelet forms the next wave front, and so the cycle continues.

Diffraction, then, can be explained by the entirety of a wave front being blocked out, but with a slit just wide enough so that exactly one point source can "fit", producing a spherical wave on the other side of the slit.

However, that raises some questions:

• The effect of diffraction is at its greatest when the slit is the exact length of the wavelength. Hence, can one assume that each point source on the wave front is spaced exactly one wavelength apart?
• Why is the diffraction effect reduced but not completely eliminated if the slit is wider than the wavelength? Surely if there is more than one wavelet that can "fit" into the slit width, then all that should be produced on the other side is another, albeit shorter, wave front. Why is it slightly bent on the sides when the original wave front is not?
• When one wavelet can fit into the slit, what happens to the rest? Do they reflect back at the boundary?
• Why are single slit diffraction patterns produced? If there is only one wavelet in the slit width, what is it interfering with to produce an interference pattern?
• I think you may be a little confused about Huygen's principle. The diffraction doesn't occur only due to one wavelet; instead, at the wavefront meeting the slits, each point on the wavefront behaves as a point source to emit wavelets. Hence you get an infinite number of point sources emitting wavelets at the slits, not just one, and the superposition of the wavelets forms the wave front. Jun 22, 2017 at 18:50
• Oh. In that case why is the diffraction effect at its greatest when the slit width is equal to the wavelength? If there are an infinite number of wavelets regardless of the width of the slit then surely how much the wave bends should be independent of the width of the slit. Jun 22, 2017 at 18:56
• "The effect of diffraction is at its greatest when the slit is the exact length of the wavelength." Can you elaborate more on this? What do you mean by "the effect of diffraction"? Jun 22, 2017 at 20:18
• @Mostafa I'm referring to the bending effect. When there is little diffraction the wave front is mostly straight but is bent at the edges. When there is a lot of diffraction the wave front is more like a semi circle. Jun 22, 2017 at 21:23
• The bending is at its maximum when the aperture is a point (not a $\lambda$ wide) and the diffracted field is a spherical wave . Jun 22, 2017 at 21:27

$$U_P(x,y) = \frac{1}{j\lambda}\iint_{\text{aperture}}U_I(x',y')\frac{\exp{(jkr)}}{r}\cos \theta \,\,ds$$
As you see from the above equation, the observed field $U_P$ 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 Huygens principle), multiplied by a factor of $\dfrac{1}{j\lambda}\,U_I(x',y') \cos \theta$. Therefore, the fictitious source located at $(x',y')$ has the complex amplitude proprtional to the incident field at that point, $U(x',y')$. This seems reasonable considering the linearity of the problem. (The presence of the remaining multiplicative factors $1/j\lambda$ and $\cos \theta$ may be explained in some other ways but not very intuitively.)