When light of wavelength $ \lambda $ falls on a thin film of thick- ness t and refractive index n, the essential conditions for the production of constructive interference fringes by the rays A and B is: (m = 1,2,3,...)

Answer (a) $ 2nt\,\cos \,r=\left( m-\frac{1}{2} \right)\lambda $

$ nt\,\cos \,r=\left( m-\frac{1}{2} \right)\lambda $

$ nt\,\cos \,r=\left( m-\frac{1}{2} \right)\lambda $

When light of wavelength $ \lambda $ falls on a th

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Considering two waves interfering at point P, having different distances. Consider a monochromatic light source ‘S’ kept at a relevant distance from two slits namely S₁ and S₂. S is at equal distance from S₁ and S₂. SO, we can assume that S₁ and S₂ are two coherent sources derived from S.
The light passes through these slits and falls on the screen that is kept at the distance D from both the slits S₁ and S₂. It is considered that d is the separation between both the slits. The S₁ is opened, S₂ is closed and the screen opposite to the S₁ is closed, but the screen opposite to S₂ is illuminating.
Thus, an interference pattern takes place when both the slits S₁ and S₂ are open. When the slit separation ‘d ‘and the screen distance D are kept unchanged, to reach point P the light waves from slits S₁ and S₂ must travel at different distances. It implies that there is a path difference in the Young double-slit experiment between the two slits S₁ and S₂.