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Diffraction Grating wavelength
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[QUOTE="Charles Link, post: 5637863, member: 583509"] Additional note: This last equation for ## \Delta \lambda ## comes from ## \Delta \theta=\frac{\Delta x}{f} ## and using ## m \lambda=d(sin(\theta)+sin(\phi)) ## with ## m=1 ## and taking a derivative which gives ## \Delta \lambda=d \Delta \theta ## (approximately). This spread of ## \Delta \lambda ## is actually what is usually observed from a spectrometer. If the slits are made very narrow, then the ## \Delta \lambda ## can approach the diffraction limit given by the first formula for ## \Delta \lambda ## in the above post. ## \\ ## ## \\ ## This first formula for ## \Delta \lambda ## is derived by using the equation for a grating of ## N ## groves ##I(\theta)=I_o \frac{sin^2(N \phi/2)}{sin^2(\phi/2)} ## where ## \phi=\frac{2 \pi}{\lambda}d ( \sin(\theta)+sin(\phi)) ## and analyzing this function to determine the resolution. This is just some additional info for you, and it should be sufficient to simply use the formula for the resolving power ## R ## provided in the previous post above. ## \\ ## ## \\ ## Incidentally, I just worked the first part of this problem and there is some ambiguity in the problem. Depending on how the diffracted angle is defined, there can be a minus sign on the ## sin(\phi) ## term in the formula. It does appear for this case that that is what they are doing and the correct answer for the order ## m ## may in fact be ## m=3 ## instead of ## m=10 ##. (The helper isn't normally supposed to provide answers, but here it is necessary to be able to discuss the complete problem.) Also, then in using the formula for ## R=Nm ##, you would use ## m=3 ##, etc. Also it is not uncommon for a diffraction grating spectrometer to be used with order ## m=3 ##, (most often ## m=1 ## is used), but generally, most measurements are not performed at an order as high as 9 or 10.(For the diffracted angle, the problem should state which side of the perpendicular to the grating it is defining as positive, i.e. it would do well to supply a diagram. Otherwise, it leaves the person solving the problem to try to guess which direction they are referring to.) [/QUOTE]
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Diffraction Grating wavelength
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