Angular width of first-order visible spectrum

Bolter · Mar 23, 2020

This is a diffraction grating problem I have been given that I am trying to answer

$Typed problem text: The wavelengths of the visible spectrum are approximately 400nm (violet) to 700nm (red). Find the angular width of the first-order visible spectrum produced by a transmission diffraction grating with 415 lines per millimeter when white light falls normally on the grating. Give your answer in degrees.$

Made a attempt at it and just wanted to see if I done this correctly or not? I get an angular width of 0.71 degrees which is very small

$Handwritten working on lined paper solving a diffraction grating problem: d sin θ = mλ, grating 415 lines/mm giving d = 2.409 × 10^-6 m, θ1 and θ2 from sin^-1 for 400 nm and 700 nm, angular width 0.71° (2 dp).$

Any help is much appreciated! Thanks

etotheipi · Mar 23, 2020

You switched from lines per millimetre to lines per centimetre at the start.

Bolter · Mar 23, 2020

etotheipi said:

You switched from lines per millimetre to lines per centimetre at the start.

Oh shoot yes you're right :doh:

I don't know what I was thinking there. This must change the whole answer then. I get my distance between adjacent slits to be 1/415,000 m = 2.409... x 10^-6 m

Running through the same process but with new d value now, I get the angular width to be 7.33 degrees now?

Angular width of first-order visible spectrum

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