Hey guys, I came across this physics question in my studies and am not sure what the answer is.

A spectral line of known wavelength (5.792*10E-7) emitted from a mercury vapour lamp is used to determine the spacing between the lines ruled on a plane diffraction grating. When the light is incident normallyhon the grating, the third-order spectrum, measured using a spectrometer, occurs at an angle of 60 degrees and 19 minutes to the normal. Calculate the grating spacing.

This question i can do but the next part i am not sure of:

Why is the value obtained using the third-order spectrum likely to be more accurate than if the first-order were used?

 

Could this be because the third order specturm is further spaced from the normal so that measuring the distance from the center of the 3rd order beam is not as important? Like measuring the distance with and error of 2 mm is far worse in the 1st order spectrum than with the 3rd order spectrum with the same 2 mm of error?

 

Consider the rules of error analysis.. You must provide an uncertainty of no less than half a measured unit.. Therefore, measuring the greater distance to the third order fringe means that the uncertainty will comprise a smaller percentage of the whole..
Further fringes would be even better as long as they are well defined, but higher order fringes tend to get fuzzier, so for the most accurate measurement overall, third may be a good general starting point..

 

so i was right then... COOL!