# 2 slits : diffraction always "enveloppe" of interference ?

• DoobleD
In summary, in the double-slit diffraction experiment, two interferences are observed simultaneously: diffraction interference from each single-slit and double-slit interference. The intensity of the light reaching the screen behind the slits appears as the product of both equations for the single-slit diffraction and for the double-slit interference. The diffraction acts as an envelope for the double-slit interference, and the width of the single-slit envelope is inversely proportional to the width of the slit(s). In a multiple-slit setup, the spacing between the interference maxima is inversely proportional to the spacing between the slits, which must be larger than the width of the slits. This ensures that the spacing between each pair of
DoobleD
In the double-slit diffraction experiment, two interferences are observed simultaneously : diffraction interference from each single-slit, and double-slit interference (where in the double-slit interference, diffraction is ignored because we considered theoretical slits way smaller than wavelength).

Intensity of the light reaching the screen behind the slits then looks like that :

My questions are :

1 - why is it the diffraction part the envelope of the double slit interference, and not the other way around ?
2 - Is it actually always in this way only ?

I've looked at 5 textbooks (undergrad level) and none of them justifies that. They all say something like : the diffraction act as an envelope, and the corresponding equation is the product of both equations for the single-slit diffraction and for the double-slit interference together.

Actually it kind of makes sense somehow because in the other way around, well, the light due to double-slit interference does not decrease in intensity on "left" and "right" of the screen. So I guess somehow, only the diffraction interference part, which has a decreasing intensity, can be the envelope. But that "somehow" is not really physical, I can't see the logical/physical justification of it.

The width of the single-slit envelope varies inversely with the width of the slit(s): wider slits produce a narrower envelope and vice versa. Similarly, the spacing between the interference maxima varies inversely with the spacing between the slits.

In a multiple-slit setup, the spacing between the slits (center to center) has to be larger than the width of the slits, so the spacing between the interference maxima has to be smaller than the width of the diffraction envelope.

DoobleD
jtbell said:
The width of the single-slit envelope varies inversely with the width of the slit(s): wider slits produce a narrower envelope and vice versa. Similarly, the spacing between the interference maxima varies inversely with the spacing between the slits.

In a multiple-slit setup, the spacing between the slits (center to center) has to be larger than the width of the slits, so the spacing between the interference maxima has to be smaller than the width of the diffraction envelope.

Very clear answer, as usual, thank you !

You wrote "the spacing between the slits (center to center) has to be larger". Why does it have to be that way? If we imagine a setup with space between slits shorter than width of each slit, then the envelope would be the slits interference instead of the diffraction right?

EDIT : I just realized that when measuring the spacing between the slits center to center, indeed the distance measured that way cannot be smaller than the width of the slits. Thus, the distance between each pair of wavelet source (one in each slit) is always greater than the width of one slit. You can ignore my last question, sorry.

## 1. What is the "enveloppe" of interference in the double slit diffraction pattern?

The "enveloppe" of interference in the double slit diffraction pattern refers to the overall shape or pattern of the interference fringes that are produced when light passes through two slits. It is the envelope of the maximum and minimum intensity points created by the overlapping of the diffracted waves from the two slits.

## 2. How is the "enveloppe" of interference affected by the distance between the two slits?

The "enveloppe" of interference is affected by the distance between the two slits in a double slit diffraction setup. As the distance between the slits increases, the overall width of the interference pattern also increases, resulting in a wider "enveloppe" of interference. Conversely, when the distance between the slits decreases, the interference pattern becomes narrower, leading to a smaller "enveloppe" of interference.

## 3. Does the wavelength of light affect the "enveloppe" of interference in double slit diffraction?

Yes, the wavelength of light does affect the "enveloppe" of interference in double slit diffraction. As the wavelength of light increases, the distance between successive bright fringes in the interference pattern also increases, resulting in a wider "enveloppe" of interference. Conversely, when the wavelength of light decreases, the distance between bright fringes decreases, leading to a smaller "enveloppe" of interference.

## 4. What is the relationship between the "enveloppe" of interference and the number of slits used in a diffraction setup?

The "enveloppe" of interference is directly related to the number of slits used in a diffraction setup. In general, the more slits there are, the narrower the "enveloppe" of interference becomes. This is because the interference pattern becomes more complex and the bright fringes become sharper when multiple slits are present, resulting in a narrower "enveloppe" of interference.

## 5. Can the "enveloppe" of interference be modified in a double slit diffraction setup?

Yes, the "enveloppe" of interference can be modified in a double slit diffraction setup by changing the parameters of the system. For example, the distance between the slits, the wavelength of light, and the size of the slits can all affect the shape and size of the "enveloppe" of interference. Additionally, placing a polarizing filter in front of the double slit can also modify the "enveloppe" of interference by altering the polarization of the light passing through the slits.

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