Question about two interference patterns viewed at infinity

[AymericNgy]

TL;DR Summary

What distance for considering that interference pattern is at infinity : do we need to consider that the interference pattern is much bigger than the size of the interfering object

Hello,
It seems like we use two different set of hypotheses to consider that we are at infinity in optics and I would like to know which one is correct.

In the case of Young's interference experiment we can see the interference pattern at infinity when a<<D and x,y<<D, with "a" the distance between the holes, "x","y" the size of the interference pattern on the screen and "D" the distance between the screen and the holes.

In the case of a diffracted light by aperture of size a with a screen at distance D and a interference pattern of size x,y, if we do the hypotheses that a<<D and x,y<<D we are in the case of Fresnel diffraction, and it's not considered to be at infinity. To considered we are at infinity we need to do the hypothese that x,y>>a, and we are in this case in Fraunhofer diffraction.

Therefore, I would like to know if we need to have x,y>>a to be at infinity, and what does it mean exactly to be at infinity for a diffraction pattern.
Thank you very much for your help.

 

[sophiecentaur]

TL;DR Summary: What distance for considering that interference pattern is at infinity : do we need to consider that the interference pattern is much bigger than the size of the interfering object

and what does it mean exactly to be at infinity for a diffraction pattern.

The pattern is an 'angular' one and has to be revealed on a screen and the fringe spacing would be high and very low in brightness. Same problem for any arrangement of lenses, which would just reduce the width of the fringes so where would that get you?

 

[sophiecentaur]

@AymericNgy : There is no 'image' as such because an image is where the various light paths converge or appear to diverge from. There is no fringe pattern 'to see'. If you look in the direction of the originating slits you will just see two slits against a black background. Your eye may not be able to resolve the two slits. If you move your head from side to side, you will move across the pattern and the brightness of the slits will appear to change because the fringes are of a similar size to your pupil (or much bigger) and the image on the retina will be just the slits and not fringes.

 

[Ibix]

Note: it is quite easy to set up the experiment @sophiecentaur describes. However, if you want to do it, I would advise using a camera instead of your eye to view the pattern directly. I think ( apparently incorrectly - see Andy Resnick's post below) most laser sources available "over the counter" say they are class I, and it should be safe to look directly down the barrel of a class I laser. But I don't know how carefully power levels are checked or who does it, so I would not bet my sight on the honesty of a commercial manufacturer's labelling.

 

[sophiecentaur]

But I don't know how carefully power levels are checked or who does it

Type approval?

 

[Andy Resnick]

Note: it is quite easy to set up the experiment @sophiecentaur describes. However, if you want to do it, I would advise using a camera instead of your eye to view the pattern directly. I think most laser sources available "over the counter" say they are class I, and it should be safe to look directly down the barrel of a class I laser. But I don't know how carefully power levels are checked or who does it, so I would not bet my sight on the honesty of a commercial manufacturer's labelling.

I have to interject here- most laser pointers are definitely not eye-safe. A 1 mW laser source, if viewed directly, appears brighter than the sun and will damage your eye if you do not blink.

References: Sliney and Wolbarsht "Safety with Lasers and Other Optical Sources", ANSI Z-136 specifications, and this helpful table: https://www.lasersafetyfacts.com/laserclasses.html

 

[Ibix]

Definitely use a camera then!

 

[sophiecentaur]

I have to interject here- most laser pointers are definitely not eye-safe.

How much power would actually get through two small slits? The beam from a laser pointer would illuminate a far larger area than the slit area.

Things were much easier when we used a discharge tube for a source.