Fresnel Diffraction through a straight edge

[Vaibhav DixiT]

I read in texts that when a rays of light are diffracted from a straight edge, the phenomenon can be explained using the half period zones.

The things that is confusing me is this: "Odd number of half period zones, if exposed, lead to a bright fringe. Even number of half period zones exposed lead to a dark fringe on the screen"

can anyone shed some light on this?

 

[sophiecentaur]

I thought that 'zones' were used in analysing diffraction in circular apertures and not straight edges. Do you have a reference?

 

[Vaibhav DixiT]

I thought that 'zones' were used in analysing diffraction in circular apertures and not straight edges. Do you have a reference?

My bad, I wrote straight edge by mistake.

 

[Zarqon]

My bad, I wrote straight edge by mistake.

You have to look at the definition of a 'zone'. The further out from the center the light goes, the longer distance it has to travel, which shows up in the end on the screen as a phase shift of light, thus larger shifts the further out it went. The first zone is simply the light that is within one half of a period phase shift from each other, meaning it can approximately be assumed to be in-phase, giving a maximum. Then, the second zone, also comprising one half of a period, will then be approximately out of phase with the first zone (since all the rays from the second zone lies outside, they travel longer distance and have larger phase shift, one half more phase shift according to the definition). If you count the two inner zones, or any even number they will be roughly out of phase all together and thus give a minimum.

Is that enough of an explanation?

 

[sophiecentaur]

Odd number of half period zones, if exposed, lead to a bright fringe.

Can you give a reference to this please? Where is the "fringe" that they produce, in this statement? Do you mean a centre spot or a ring around it? The diffraction pattern will always have the same total amount of light and it just depends upon where you get constructive interference and where not.
How familiar are you with two slit diffraction and the way a simple diffraction grating works? In the case of a zone plate, you are dealing with a two dimensional array of sources (and the pattern requires integration to calculate it, unlike a simple array of point sources) But you can identify where maxes and mins are going to occur.
http://depts.washington.edu/jrphys/ph331/share/zone.pdf which (to me) seems to give a reasonable answer to your question.