Diffraction grating question - help needed please

4. A diffraction grating is designed with a lit width of 0.83 micrometers. When used in a spectrometer to view light of wavelength 430nm, diffracted beams are observed at angles of 14 degrees 55' and 50 degrees 40' to the zero order beam.

a.Assuming the low-angle diffracted beam is the first order beam, calculate the number of lines per mm on the grating.

b. explain why there is no diffracted beam between the two observed beams - what is the order for the beam of 50 degrees 40'

You are given
$d$, the "slit width", which for a grating they probably mean the grating spacing.
$\lambda$ the wavelength of the light, and
$\theta$=14"55' for the 1st order diffraction.
The 1st order (where n=1) is the one where a single whole wavelength fits in the space AB in the diagram, causing the beams to be in phase and produce constructive interference; and a bright fringe.
The formula is $n\lambda = d sin \theta$
The next angle given must be for the case where n=2 and there are two wavelengths difference between the beams.
For the question, you are just asked for how many lines per mm there are on the grating. As you are told in the question that the "slit width" is 0.83 micrometers, the number per mm is $\frac{1}{width}$ where the "width" is also in mm.

Note, the diagram only shows 2 adjacent slits. There are hundreds in a grating, all equally spaced.

You are given
$d$, the "slit width", which for a grating they probably mean the grating spacing.
$\lambda$ the wavelength of the light, and
$\theta$=14"55' for the 1st order diffraction.
The 1st order (where n=1) is the one where a single whole wavelength fits in the space AB in the diagram, causing the beams to be in phase and produce constructive interference; and a bright fringe.
The formula is $n\lambda = d sin \theta$
The next angle given must be for the case where n=2 and there are two wavelengths difference between the beams.
For the question, you are just asked for how many lines per mm there are on the grating. As you are told in the question that the "slit width" is 0.83 micrometers, the number per mm is $\frac{1}{width}$ where the "width" is also in mm.

Note, the diagram only shows 2 adjacent slits. There are hundreds in a grating, all equally spaced.

Stone, may i ask you a follow up?
what about part b on this
why isn't there a wave in the 3rd order or something of the sort?
tyvm

You are given
$d$, the "slit width", which for a grating they probably mean the grating spacing.
$\lambda$ the wavelength of the light, and
$\theta$=14"55' for the 1st order diffraction.
The 1st order (where n=1) is the one where a single whole wavelength fits in the space AB in the diagram, causing the beams to be in phase and produce constructive interference; and a bright fringe.
The formula is $n\lambda = d sin \theta$
The next angle given must be for the case where n=2 and there are two wavelengths difference between the beams.
For the question, you are just asked for how many lines per mm there are on the grating. As you are told in the question that the "slit width" is 0.83 micrometers, the number per mm is $\frac{1}{width}$ where the "width" is also in mm.

Note, the diagram only shows 2 adjacent slits. There are hundreds in a grating, all equally spaced.

what does the bit in bold mean? xx

what does the bit in bold mean? xx

Wow this is from 10 years ago.
It's from the 2nd line in the original question and means
14 degrees 55 minutes
I should have written 14^o 55'
Sorry for any confusion.

1 arcminute is a 60th of a degree

Thank you! I guess its not on the new spec because I'm not aware of it xx