Why Does a Diffraction Grating Not Show Intermediate Intensity Patterns?

[Blistering Peanut]

Since I'm on a roll,

http://img9.imageshack.us/img9/9734/untitled.jpg

Laser shining through a diffraction grating produces several bright spots according to

$$n \lambda = d sin\theta$$

I was wondering when the path difference isn't equal to or a multiple of the wavelength, why don't we see a pattern more like the one on the top right, with slightly constructive interference and completely destructive intereference halfway between each dot?

 

[ZapperZ]

Since I'm on a roll,

http://img9.imageshack.us/img9/9734/untitled.jpg

Laser shining through a diffraction grating produces several bright spots according to

$$n \lambda = d sin\theta$$

I was wondering when the path difference isn't equal to or a multiple of the wavelength, why don't we see a pattern more like the one on the top right, with slightly constructive interference and completely destructive intereference halfway between each dot?

OK, since no one is tackling this one, I will foolishly jump in! :)

Let me start with the single slit pattern and we'll see if I can explain the trend here as you add more and more slits. In a single slit, what you have is a Fraunhoffer pattern. You have a central bright "glob", followed by dark-bright-dark-etc globs. This is exactly what you were looking for, but for a single slit, i.e. you have varous degree of intensity in the pattern.

Now, let's add another slit to this, so we have a 2-slit case. What you now have is an ADDITIONAL set of interference pattern that is modulated by the ORIGINAL single-slit fraunhoffer pattern. In other words, the "criteria" for complete constructive and complete destructive is now more stringent. At the same time, the modulation of the intensity imposed by the original single-slit is still there.

You can tell that as you add more and more slits, only the constructive peaks will be the one most apparent TO YOUR EYE. The rest of the "in betweens" are there, but they are mostly washed out. Their intensities are still there, but your eye isn't sensitive enough to detect them. We know this because in X-ray diffraction experiments where the angular diffraction are scanned by photosensitive detectors, these "in-between" intensities are still present but highly diminished in strength when compared to the constructive peaks.

http://www.phy.davidson.edu/StuHome/grpatterson/Diffraction and Spatial Filtering/double_slit1.htm

http://scienceworld.wolfram.com/physics/DiffractionGrating.html

Zz.