Observing Spectral Lines: The Highest Order & Color Sequence

[elevenb]

Homework Statement

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?

Homework Equations

mλ=dsinθ

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?

 

[ehild]

Homework Statement

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?

Homework Equations

mλ=dsinθ

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?

The result is correct, but the physicist observes angles. It does not change the order as the sine function is monotonously increases with your multiples of wavelengths.

ehild