 ### Question

You are watching: A commercial diffraction grating has 400 lines per mm.   Dictionary Calculator ## A diffraction grating has 400 lines per mm and is illuminated normally by monochromatic light of wavelength 6000 Å. Calculate the grating spacing, the angle at which the first-order maximum is viewed and the maximum number of diffraction maxima are obtained.

A diffraction grating has actually 400 lines per mm and is illuminated generally by monochromatic light of wavelength 6000 Å. Calculate the grating spacing, the angle at which the first-order maximum is checked out and the maximum variety of diffraction maxima are derived.

Solution

Given,

Grating room (d) = ?,Number of lines (N) per mm = 400 lines/mm = 400,000 lines/m,(d=frac1N=frac1400000=2.5 imes10^-6) mWavesize, (lambda=6000Å=6000 imes10^-10) m

We have actually,

(dsinleft( heta ight)=nlambda)

So for the first order,

(dsinleft( heta_1 ight)=lambda=6000 imes10^-10)(Rightarrow heta_1=13.85^circ)

For the maximum number of the diffractivity maxima, θ = 90°

∴ (n=frac dlambda=frac2.5 imes10^-66000 imes10^-10=4.17approx4)

Hence the maximum number of maxima grating acquired is 4.

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