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.

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Navjyot Kalra · Answer

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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