Diffraction question - How do I approach this?

Question:
Blue light of wavelength 485.6nm from a star is incident normally on a diffraction grating. The light is diffracted into a number of beams, as shown in Fig 5.4.

The angular separation of the two second-order beams is 45.72 degrees.
Calculate the number of lines per millimetre on the grating.

I do not even know where to start the question. I know the formula for Young's double slit experiment however this does not seem to relate to it at all. Any suggestions for starting the question would be really appreciated.

Reply 1

Stonebridge

It's not Young's double slits it's a diffraction grating, for which there is a formula that will be in your book or your notes.
It contains terms including the angles in the diagram, the wavelength of the light and the spacing of the lines in the grating.

Reply 2

leosco1995

I think I can answer this. The formula for diffraction grating is,

d sin θ = nλ

Where d = spacing of the lines, θ is the angle of the nth order from the undeviated beam, n is the order # and λ is the wavelength. Here we have to find n which is equal to 1/d,

d sin 22.86 = 2 * 485.6 * 10^-9
d = 2.5 * 10^-6

Lines per m = 1/d = 400000
Lines per mm = 400

I hope that's the right answer.

Reply 3

Micky76

Original post by leosco1995

I managed to solve it after finding the equation. Worked out the same as your answer. The question was from an old past paper and I didn't cover diffraction gratings since its no longer on the spec. Thanks for the help.