Question #247855
a system of grating has two wavelength 5.0 x 10^-7 and 5.2 x 10^-7m. the focal length is 2.0n and the grating separation is 2.0×10^-6m find the change in linear separatiom per unit increase in the specttal order of two wavelength
1
Expert's answer
2021-10-07T09:45:36-0400

Write down the conditions for maxima and determine the angle:


dsinθ1=mλ1,dsinθ2=mλ2. θ1=arcsinmλ1d, θ2=arcsinmλ2d.d\sin\theta_1=m\lambda_1,\\ d\sin\theta_2=m\lambda_2.\\\space\\ \theta_1=\arcsin\frac{m\lambda_1}{d},\\\space\\ \theta_2=\arcsin\frac{m\lambda_2}{d}.

For the length between the grating and screen 2.0 m, find the change in linear separation:


Δz(m)=D(tanθ2tanθ1)= =D(tanarcsinmλ2dtanarcsinmλ1d)= =2[tanarcsin(0.26m)tanarcsin(0.25m)].\Delta z(m)=D(\tan\theta_2-\tan\theta_1)=\\\space\\ =D(\tan\arcsin\frac{m\lambda_2}{d}-\tan\arcsin\frac{m\lambda_1}{d})=\\\space\\ =2[\tan\arcsin(0.26m)-\tan\arcsin(0.25m)].


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