Adiffraction grating is made up of slits of width = 340 nm with separation = 790 nm. the grating is illuminated by monchromatic plane waves of wavelength λ = 520 nm at normal incidence. a. how many maxima are there in the full diffraction pattern?
b. what is the width of a spectral line observed in the first order if the grating has 500 slits? (deg)

angular width is  0.10 degree

Explanation:

Given data

width = 340 nm

separation d = 790 nm

λ = 520 nm

to find out

how many maxima and width of a spectral line

solution

we know for maxima formula is

m λ = dsinθ

and we know here sinθ is between 0 and 1

so we can say

d is greater than m λ

and

m ≤ d / λ

m ≤ 790 / 520

m ≤ 1.52

its mean we have 3 maxima i.e. 0 , 1 and -1

and

for 1st order m = 1

so mλ  = dsinθ

λ  = dsinθ

θ = sin^-1 ( λ/d)   ................................1

and angular width is

θ = λ/ Nd cosθ

θ = dsinθ / Nd cosθ  

θ = tanθ /N              ...............................2

so here put θ in 2 equation

angular width = tanθ/N

angular width = tan ( sin^-1 ( 520/790) ) / 500

angular width = tan 41.16 / 500

angular width = 1.7484 ×      × 180/π

angular width =  0.10 degree