Single slit diffraction bright fringe's width

[Koveras00]

According to my knowledge, the position of the dark fringes is given by

asin(x)=m*lamda (sorry, I do not know how to type equations in here)

tan(x)=d/L

a=slit width
x=angle of diffraction(?)
m=no. of order
d=distance from the central fringe
L=distance between slit and screen

By using is equation, I found out that the distance between successive dark fringes is increasing as the order increase. Which means that the width of the bright fringes increase with the order.

But, from this webpage (last section), http://dev.physicslab.org/Document....me=PhysicalOptics_InterferenceDiffraction.xml

Quote:
"In a diffraction pattern, the central maximum has the greatest brightness, with each successive bright fringe getting narrower and dimmer."

Which says the opposite. Tried searching the web and this forum but couldn't find any info.

Please advice. Thank you.

 

[cesiumfrog]

It's the paraxial approximation you should search for.

If you have trouble still, since you haven't actually seen the pattern yourself, try putting reasonable values into your equation (10 metres, 500 nanometres, 1st through to 10th orders, 50 micrometres), and then tell us again whether you still find any contradiction.

..not quite sure what the webpage you quoted actually meant.

 

[Koveras00]

I tried plugging in values in the equation, that is how I found out that the separation of successive dark fringes increases as the order increases. Bright fringes exist between the minimas hence the width of the bright fringes decreases too.

I have also seen and tried measure the width of the bright fringe using a photometer.

All points towards that the width of the bright fringes will increases when the order increases.

But after bumping into the website that I have quoted, I begin to doubt my understanding of single slit diffraction and my experiment. Therefore posting this thread. The picture in the website also show that the separation of dark fringes decreases.

Sorry if I could not explain myself well.

 

[cesiumfrog]

Give the numbers you calculated (to better facilitate us pointing out the insignificance of the variation). Remember to use the correct number of significant figures (the data I specified has but 1 or 2).

 

[Claude Bile]

I think the site is wrong - the ideal single-slit diffraction pattern is a sinc^2 pattern, which means that ideally at least, all the maxima should be spaced equally far apart. Deviation from the ideal case should result in higher order maxima being spaced further apart (as the paraxial approximation becomes less suitable for higher order maxima).

Take a look at the photo here of the diffraction of an x-ray wave by a single rectangular slit;

http://www.elettra.trieste.it/science/elettranews/volume46/en110.html

Clearly the spacing of each maxima is uniform across the first 7-8 orders, at higher orders the increase in separation is also evident.

Claude.

 

[cesiumfrog]

Take a look at the photo here [..] at higher orders the increase in separation is also evident.

I disagree with that interpretation of your data. It appears to me to demonstrate that separation between successive maxima (or minima) remains constant (at least within the precision of the image). It also demonstrates each successive fringe appearing narrower, as per the website quote (although I suspect this effect is mainly to do with the perception of brightness gradients).

 

[Claude Bile]

To me, the separation appears to increase for the vertical set of fringes at the top of the image, but I concede that it might just be an illusion.

Claude.