An 18-mm-wide diffraction grating has rulings of 710 lines per millimieter. Mono

Question

An 18-mm-wide diffraction grating has rulings of 710 lines per millimieter. Monochromatic light of wavelength 506 nm wavelength is incident normally on the grating. What is the largest angle from the centerline at which an intensity maximum is formed? An 18-mm-wide diffraction grating has rulings of 710 lines per millimieter. Monochromatic light of wavelength 506 nm wavelength is incident normally on the grating. What is the largest angle from the centerline at which an intensity maximum is formed? 46° 38° 44° 40° 42°

Please explain each step. Thank you!

Explanation / Answer

w= 18*10^-3m
N= 18*710 (because you have 710slits per mm) = 12780
lambda= 506*10^-9

The first step is to work out d.
d=w/N=18*10^-3m/12780 =1.41*10^-6m

The second step is to work out the maximum number of m.
Since sin(theta)= less than 1, then m*lambda/d= less then 1, therefore m= less than d/lambda
(I know that s confusing but trust me)
so m is less than 1.41*10^-6m/506*10^-9 = 2.7
Therefore use m=2

Lastly put it all into the formula dsin(theta)=m*lambda
so: theta=sin^-1(m*lambda/d)
theta= sin^-1(2*506*10^-9/1.41*10^-6m)
theta=45.95 degrees =46 degrees

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