Wave Optics

Two coherent sources \(S_{1}~and~S_{2}\) separated by distance \(2 \lambda\) emit light of wavelength \(\lambda\), in phase as shown. A circular wire of radius \(100 \lambda\) is placed in such a way that \(S_{1}S_{2}\) lies in its plane and the mid point of \(S_{1}S_{2}\) is at the centre of wire. The angular positions on the wire for which intensity reduces to half of its maximum value for the first time is given as \(\theta\). Find the value of \(32cos \theta\)

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