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In Young's double slit experiment width of fringe produced on the screen is β. Now one of the slits is covered with a sheet of glass μ=1.5 of thickness t=8λ where λ is the wavelength of light used. Then distance of the new position of central bright fringe from the previous position of central bright fringe is

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a

β

b

2β

c

4β

d

6β

answer is C.

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Detailed Solution

Fringe width β=λDd where D is screen separation and d = slit separation. When one slit is covered, fringe width remains unchanged and the net path difference between rays at new position of central bright fringe should be zero. ∴ μ−1t−dsinθ=0⇒dsinθ=μ−1t⇒dtanθ=μ−1t⇒d.yD=μ−1t⇒y=μ−1tλ.λDd=1.5−18λλ.β=4β

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