Hi, having trouble determining whether my lab book has made an error, or I have.(adsbygoogle = window.adsbygoogle || []).push({});

Intensity as a function of [tex]\phi[/tex] for 2 slits is given as

[tex]A^2={A_2}^2\frac{sin^2(\frac{\phi}{2})}{{(\frac{\phi}{2})}^2}cos^2(\frac{\beta}{2})[/tex]

but then it gives the amplitude for N slits to be

[tex]A^2={A_N}^2\frac{sin^2(\frac{\phi}{2})}{{(\frac{\phi}{2})}^2}\frac{sin^2(\frac{N\beta}{2})}{sin^2(\frac{\beta}{2})}[/tex]

However, when I sub in N = 2 for the equation (2), and use the double angle formula to reduce the right fraction in equation (2) I get 4*equation(1) rather than just the equation(1) alone. Am I doing it wrong?

To be more succinct, isn't [tex]\frac{sin^2(\frac{N\beta}{2})}{sin^2(\frac{\beta}{2})} = 4cos^2(\frac{\beta}{2})[/tex]?

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# Homework Help: N-slit Interference/Diffraction

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