Interference on a cylindrical screen
Two identical beams \(A\) and \(B\) of plane coherent waves of the same intensity and wavelength \(\lambda\) on a cylindrical screen. The angle between the directions of the beam propagations is \(\theta\). Consider a point \(P\) on the screen at angular position \(\phi\) from the beam \(A\) as shown in the figure. Find distance between adjacent interference fringes on the screen near the point \(P\). Assume that the distance \(\beta\) between adjacent fringes is much less than the radius of the cylinder.
If \(\sin \left ( \dfrac\theta2 \right) \cos \left( \dfrac \theta2 + \dfrac \phi 2 \right) = \dfrac \lambda 2 \). Find the fringe width at point \(P \) on the cylindrical screen.