Spectral Lines

1. The problem statement, all variables and given/known data

In a question I was asked, assuming a spectrometer reading of Hydrogen produced two strong spectral lines at 656.3nm and 410.1nm. And also assuming the diffraction grating had 500 lines/mm

What is the highest order of spectrum which can be fully observed , i.e value of m.

and assuming the physicist begins with the spectrometer telescope eyepiece at a deviation angle of zero and rotates it through 90 degrees, determine the sequence of line colours that she sees?

2. Relevant equations

mλ=dsinθ

3. The attempt at a solution

I worked out that the highest value of m for the 656.3nm line is 3 and for the 410.1nm line it’s four but because it says fully observed I said three because the two lines can be observed fully at this order of spectrum.

For the second part I wrote out multiples of the wavelengths, I got

410.1, 820.2, 1230.3, 1640.4

656.3, 1312.6, 1968.9

So if I call the 410.1nm one violet, and the 656.3nm one red. Are the colours she sees

Violet, red, violet, violet, red, violet, red?

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