Interference fringes were produced using a light of wavelength $$4800$$ $$A0$$ in a double slit arrangement. When sheet of uniform thickness of refractive index $$1.6$$ (relative$$ to $$air) is placed in the path of light from one of the slits, the central fringe moves some distance. This distance is equal to the width of $$30$$ interference bands. The thickness (in$$ μm $$) of sheet is:

Question

Interference fringes were produced using a light of wavelength $$4800$$ $$A0$$ in a double slit arrangement. When sheet of uniform thickness of refractive index $$1.6$$ (relative$$ to $$air) is placed in the path of light from one of the slits, the central fringe moves some distance. This distance is equal to the width of $$30$$ interference bands. The thickness (in$$ μm $$) of sheet is:

Infinity Learn · Accepted Answer

Shift of fringe $$pattern=$$μ−$$1tDd30$$ D $$(4800$$ × $$10$$−$$10)d=0.6t$$ $$Dd=30$$×$$4800$$×$$10$$−$$10=0.6t=30$$ × $$4800$$ × $$10$$−$$100.6=1.44$$ × $$10$$−$$50.6=24$$×$$10$$−$$6$$

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