Interference on a cylindrical screen

Classical Mechanics Level pending

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.

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