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A diffraction grating consisting of 40...

A diffraction grating consisting of 4000 slits per centimeter is illuminated with a monochromatic light that produces the second order diffraction at an angle of `30 ^(@)`. What is the wavelenght of the light used?

Text Solution

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Number of lines per cm `=4000, m=2,0=30^(@),lambda=?`
Number of lines per unit length, `N=(4000)/(1xx10^(-2))=4xx10^(5)`
Equation for diffraction maximum in grating is, `sin0=Nmlambda`
Rewriting, `lambda = (sin0)/(Nm)`
Substituting, `lambda=(sin30^(@))/(4xx10^(5)xx2)=(0.5)/(4xx10^(5)xx2)=(1)/(2xx4xx10^(5)xx2)=(1)/(16xx10^(5))`
`lambda=6250xx10^(-10)m=6250Å`
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