Optics Question 159

Question: In a double slit arrangement fringes are produced using light of wavelength 4800AA . 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

Options:

A) 8 mm

B) 6 mm

C) 4 mm

D) 10 mm

Show Answer

Answer:

Correct Answer: A

Solution:

Shift Δx=βλ(μ−1)t

Shift due to one plate Δx1=βλ(μ1−1)

Shift due to another path Δx2=βλ(μ2−1)t

Net shift Δx=Δx2−Δx1=βλ(μ2−μ1)t …(i)

Also it is given that Δx=5β …(ii)

Hence 5β=βλ(μ1−μ2)t

⇒t=5λ(μ2−μ1)=5×4800×10−10(1.7−1.4)

=8×10−6m=8μm.

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