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A monochromatic light of wavelenght of 5...

A monochromatic light of wavelenght of 500 nm strikes a grating and produces foruth order bright line at an angle `30^(@)`. Find the number of slits per centimeter.

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`lambda = 500 nm = 500 xx 10^(-9) m,m = 4 , theta = 30^(@)` , number of lines per cm = ?
Equation for diffraction maximum in grating is, `sin theta = N m lambda`
Rewriting, `N = (sin theta)/(m lambda)`
Substituting, `N=(0.5)/(4xx500xx10^(-9))=(1)/(2xx4xx500xx10^(-9))=2.5xx10^(5)` lines per meter
number of lines per centimeter = `2.5 xx 10^(5) xx 10^(-2)` = 2500 lines per centimetre
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