In a double slit arrangement fringes are produced using light of wavelength 4800 Å. One slit is covered by a thin plate of glass of refractive index 1.4 and the other with another glass plate of same thickness but of refractive index 1.7. By doing so the central bright shifts to original fifth bright fringe from centre. Thickness of glass plate is
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a
8 mm
b
6 mm
c
4 mm
d
10 mm
answer is A.
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Detailed Solution
Shift Δx=βλ(μ−1) tShift due to one plate Δx1=βλ(μ1−1)Shift due to another path Δx2=βλ(μ2−1) tNet shift Δx=Δx2−Δx1=βλ(μ2−μ1) t …..(i)Also it is given that Δx=5β …..(ii)Hence 5β=βλ(μ2−μ1) t⇒t=5λ(μ2−μ1)=5×4800×10−10(1.7−1.4)=8×10−6m=8μ m.