Interference fringes were produced in Young's $$double-slit$$ experiment using light of wavelength $$5000$$ Å. When a film of thickness $$2.5$$×$$10-3$$ cm was placed in front of one of the slits, the fringe pattern shifted by a distance equal to $$20$$ $$fringe-width$$. The refractive index of the material of the film is

Question

Interference fringes were produced in Young's $$double-slit$$ experiment using light of wavelength $$5000$$ Å. When a film of thickness $$2.5$$×$$10-3$$ cm was placed in front of one of the slits, the fringe pattern shifted by a distance equal to $$20$$ $$fringe-width$$. The refractive index of the material of the film is

Infinity Learn · Accepted Answer

Shift, Δ$$x=$$[$$($$μ−$$1)t$$]Dd⇒ $$20$$β$$=($$μ−$$1)tDd$$⇒ $$20$$λ$$Dd=($$μ−$$1)tDd$$⇒ $$20$$λ$$=($$μ−$$1)t$$⇒ μ$$=20$$λ$$t+1$$⇒ μ$$=20$$×$$5000$$×$$10$$−$$102.5$$×$$10$$−$$5+1$$⇒ μ$$=410+1$$⇒ μ$$=1.4$$

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