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Let me briefly respond to this relevant comment on Skewed Definitions:
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JKMSMKJ has left a new comment on your post "Skewed Definitions":
How is it 'too late' to publish something? (Given that it hasn't been published already.) ...Or how about 'publishing' on the blog itself, removing all the middle-men!
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After a couple of decades of teaching Physics at IIT KGP, I discovered that any question on UG Physics that takes more than 24 hours of intense worrying makes for a short Note in one of the well-read teaching journals.
And I was right most of the time.
One such question that bothered me while I was setting the Question Paper for the Jumbo First Years towards the end of my stay at KGP had to do with the Chromatic Resolving Power (CRP).
It is entirely academic and not at all important practically but shows how we often tend to forget the derivations of formulae we take for granted, and how that can lead to confusion.
I talked about it in one of my earlier blogs; but I suspect that there are now a few new KGPhians reading this blog once in a while.
So, here it is:
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It is well-known that there is a stunningly simple formula for the CRP of a simple grating at normal incidence:
CRP = mN (where m is the order and N the total number of lines in the grating).
Now double slit is the simplest 'grating' with N = 2.
So, its CRP = 2m.
But it is nonsense, because double slit can't resolve at all; its 'CRP' is zero in all orders.
Because for a double slit the bright and dark fringes are equally wide...try it and see.
This is because there is a thing called Rayleigh Criterion that we use in deriving the CRP formulae; and forget thereafter.
This requires that the 'spectral lines' should be narrow enough to make sense.
How narrow?
In other words, at what minimum value of N does the CRP formula start making sense?
To get the answer, we have to draw superposed plots for closely lying 'spectral lines' with increasing 'delta lambda' for N = 2, N = 3, and so on and watch.
This is not as easy as it seems...it requires the patience of a mini-Tycho Brahe.
And I am a lazy lubber.
And then KK arrived in the Department and started as my partner in Jumbo Teaching.
And he had a powerful PC and knew programming (I forgot my Fortran II learned 35 years ago then).
And I gave the problem to him.
And after much 'graphing', we saw that the minimum number of slits N in the 'grating' that makes the CRP formula somewhat sensible is around N = 6 or so...I forget.
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3 comments:
KK once told me about this problem & its origin and ended the 'story' with two points:
1) You need to do a bit of programming to get the answer (As expected, he didn't tell me the answer and I never got around to programming!);
2) You can ask GPS for the answer, he knows it!
Better late than never, I suppose... :)
I feel that the definitions based on Rayleigh-like criteria (or visual appearance of some pattern) need some slight revision. The back end of spectrometers is now typically a sensitive linear CCD pixel array. And it is common for these digital-data-acquiring spectrometers to perform some amount of deconvolution to improve on what is seen visually.
An important aspect of the quality of such deconvolution or deblurring is the Signal-to-Noise ratio in the measurement. With a high SNR pixel array (e.g. cooled CCD) and a robust deconvolution algorithm, small number of slits may be able to resolve two lines
that are closer than Rayleigh criterion.
I think you should publish this result. Just my opinion.
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