Answer to Question #172591 in Optics for Shraddha kesarwani

Question #172591

calculate the minimum number of lines that a grating must have to resolve sodium doublet(5890A and 5896A) in third order.



1
Expert's answer
2021-03-18T15:35:21-0400

Resolving power of grating is given by:

λΔλ=nN\frac{\lambda }{\Delta \lambda }=nN

n=orderofgratingn=order\:of\:grating

N=numberoflinesofgratingN=number\:of\:lines\:of\:grating

Heren=3   Here\:n=3\:\:\:


N=λ3ΔλN=\frac{\lambda }{3\Delta \lambda }


Δλ=58965890=6\Delta \lambda =5896-5890=6


N=(5896+58902)3×6N=\frac{\left(\frac{5896+5890}{2}\right)}{3\times 6}


N=589318N=\frac{5893}{18}


N=327N=327

Minimum number of lines== 327


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