# Why should the light source be bigger in division of amplitude than the slit in division of wavefront?

Division of amplitude is a method of achieving interference using two waves that have come from the same point on a wavefront. Each wave has a portion of the amplitude of the original wave. In order to achieve interference by division of amplitude, the source of light must come from a much bigger source than the slit used for division of wavefront interference. The image produced will, however, be "localized" to one place instead of being found anywhere in front of the sources.

Why would this be the case? Perhaps it's a wording issue, does someone mind explaining?

The textbook teaches interference in division of wavefront and division of amplitude, using single slit diffraction and thin film interference as examples. Here is the text in context:

## Interference By Division of amplitude

It was mentioned in the introduction to this sub-topic that there are two ways of providing coherent sources that are able to interfere. Young's double slit and multiple slits all derive their interfering waves by taking waves from different parts of the same wavefront. Because the interfering waves have all come from the same wavefront they will be in phase with each other.

Wherever the waves meet they will interfere and a fringe pattern can be obtained anywhere in front of the sources (the slits). Since this interference can be found anywhere the fringes are said to be "non-localized".

Division of amplitude is a method of achieving interference using two waves that have come from the same point on a wavefront. Each wave has a portion of the amplitude of the original wave. In order to achieve interference by division of amplitude, the source of light must come from a much bigger source than the slit used for division of wavefront interference. The image produced will, however, be "localized" to one place instead of being found anywhere in front of the sources.

There is not enough context to fully interpret the quote. However, the statement appears to be incorrect or misleading.

Edit 6/26/20: There is some ambiguity in the meaning of "source". If a laser beam is spread out to a diameter of 1 foot, then passed through a diffuser, what is the source? Is it the original laser beam, or is it the 1 foot spot on the diffuser? In fact, the light downstream from the diffuser can be "unscrambled" and brought to a point focus, so I'd say in this case it makes sense to say that the "source" is effectively a point.

Often the size of a source refers to amount of incoherence: the smallest spot the light can be focused down to. The size of that spot is a function of both temporal and spatial incoherence. To make a decent interferometer, it is important for the size of source in that sense to be small - regardless of whether it is a wavefront division interferometer or an amplitude division interferometer.

Wavefront division can be accomplished by a pair of mirrors, each placed in a different half of a spread-out beam. Amplitude division is accomplished by passing a beam through a beamsplitter, reflecting a fraction of the beam's amplitude in one direction and allowing the other fraction to transmit through the beamsplitter.

The size of the original source in both cases should be small for best results. "From the same point on a wavefront" would be infinitesmally small, because a point is small by definition.

Spreading the beam for wavefront division is easily done using a lens; and spreading the beam to the same size for amplitude division can easily be done before or after the beamsplitter.

• I added more context to my question, have a look. Also, could you please explain your answer in more detail, I fail to understand how the fact that " "From the same point on a wavefront" would be infinitesimally small." implies that the light source should be small for both division of wavefront and division of wavelength. On your last paragraph do you argue that it's convenient to have a small beam because later we can "spread" it out using lenses? but if so, isn't this process not required in some types of wavefront and wavelength divisions like slit diffraction and thin film interference? Jun 26, 2020 at 12:33
• I've edited my answer, hopefully making the explanation clearer. Jun 26, 2020 at 15:44

I think the author is trying to ensure that there are enough photons from many angles in order for the Huygens "interference" explanation to work. Water waves are made of many atoms and behave en masse, photons behave as individuals and many DS experiments actually use single photons! With single photons the pattern still emerges which questions the historical Huygens/interference explanation. A much better explanation is Feynman's. Both explanations work well mathematically but the Huygens one (still mostly taught today) does not work for the single photon experiments done in the 1960s.

• That's very interesting, but I don't see why division of wavelength happening with just one photon would contradict Huygens principle, because as far as I know Huygens's principle is used to explain slit interference (division of wavefront) not division of amplitude interference, such as with thin films. As stated in my question: "In order to achieve interference by division of amplitude, the source of light must come from a much bigger source...", you say the book tries to "ensure that there are enough photons from many angles" but that's not needed on division of amplitude interference. Jun 30, 2020 at 12:22