Problem 17.48 A miniature spectrometer used for chemical analysis has a diffract

Question

Problem 17.48

A miniature spectrometer used for chemical analysis has a diffraction grating with 800 slits/mm set 25.0 mm in front of the detector "screen." The detector can barely distinguish two bright lines that are 30 m apart in the first-order spectrum.

What is the resolution of the spectrometer at a wavelength of 550 nm ? That is, if two distinct wavelengths can barely be distinguished, one of them being 550 nm , what is the wavelength difference between the two?

Express your answer to two significant figures. Units are in nm

Explanation / Answer

Given that

The diffraction grating slits(N) =800slits/mm =800*103slits/m

The order of the spectrum is (n) =1

We know that the resolving power of a grating is given by

Lamda/Dletalamda =nN

Lamda/Dletalamda =nN =(1)(800*103slits/m)=800*103

Now the diffrence in wavelength is given by

Deltalamda =nNlamda =nN*lamda =(800*103)(500*10-9m)=40*10-2=0.40m

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