(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Light consisting of two nearly equal wavelengths L and L+dL, where dL << L, is incident on a diffraction grating. The slit separation of the grating is D. Show that the angular seperation of these two wavelengths in the m'th order is dTheta = dL / ((D/m)^{2}+L^{2})^{0.5}

2. Relevant equations

D sin(Theta) = mL (m=0,+-1, +-2,...)

3. The attempt at a solution

D sin(Theta1)=m(L+dL)

D sin(Theta2)=m(L)

dTheta = sin(Theta1)-sin(Theta2) = (m/D)(L+dL-L) = (m/D)dL= dL/(D/m)

This answer doesn't match the formular I need to proof: dTheta = dL / ((D/m)^{2}+L^{2})^{0.5}

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# Homework Help: Diffraction grating angular separation

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