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A plate of thickness t made of a material of refractive index μ is placed in front of one of the slits in a double slit experiment. (a) Find the change in the optical path due to introduction of the plate. (b) What should be the minimum thickness t which will make the intensity at the centre of the fringe pattern zero? Wavelength of the light used is λ. Neglect any absorption of light in the plate.
Sol. a) Change in the optical path = μt – t = (μ – 1)t b) To have a dark fringe at the centre the pattern should shift by one half of a fringe. ⇒ (μ – 1)t = λ/2 ⇒ t = λ/2(μ – 1)
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