How to interpret the diffraction envelope

[Bill Sellers]

Explanations of 2-slit interference sometimes show the interference pattern compared to a 1-slit diffraction pattern, and state that the latter represents a limit or envelope for the former. Is it correct to interpret the patterns as representing (directly or indirectly) the number of photons being detected at locations on the screen? If so, then wouldn’t this imply that fewer photons are detected in the 2-slit setup vs. 1-slit?

 

[kuruman]

If so, then wouldn’t this imply that fewer photons are detected in the 2-slit setup vs. 1-slit?

When you compare number of photons to the screen between a single slit and a double slit experiment, you need to specify what is the same and what is different. Of course the source intensity is the same but what about the slit width? If the same number of photons per unit time goes through the double slit arrangement as goes through the single slit, then you should collect the same number of photons at the screen.

 

[Bill Sellers]

Thank you very much for taking the time to respond to my query. I'm trying to understand a graphic such as the one at http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/dslit.html. I'm guessing that the single slit envelope shows the pattern you'd get if you closed one of the slits and doubled the width of the remaining one. If that guess is correct, then presumably the same number of photons per unit time should be going through. But the interference pattern doesn't seem to reflect that--it seems to be showing fewer photons.

 

[Cthugha]

Such graphs are usually normalized to the peak intensity, so the absolute values of the count rates are not comparable.

As a rule of thumb: If you have one slit of a certain width which is illuminated with a certain intensity and now change to a different setting with two slits close to each other, where each of the two slits gets the same intensity as the single slit and has the same size, you will have twice the field in the area of constructive interference (if it is located in the middle between the slits). Accordingly, the peak intensity will be 4 times as high as before. If you use 3 slits, it will be 9 times as high. If you use many slits...you have just built a diffraction grating.

 

[Bill Sellers]

4 times--thanks, that makes sense!