Question

A diffraction 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)

Answer 1

angular width is 0.10 degree

Step-by-step 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 ×
`10^(-3)` × 180/π

angular width = 0.10 degree