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Question

Monochromatic light of wavelengths 400 nm and 560 nm are incident simultaneously and normally on double-slit apparatus whose slit separation is 0.1 mm and screen distance is 1m. Distance between areas of total darkness will be ___ mm

A
4
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B
5.6
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C
14
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D
28
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Solution

The correct option is D 28
Given:
Wavelengths, λ1=400nm=400×109m,
λ2=560nm=560×109m
Slit separation, d=0.1mm=0.1×103m
Screen distance, D=1m
To find:
Distance between areas of total darkness, Δs=?
According to the question,
(2n+1)λ1=(2m+1)λ2(2n+1)(2m+1)=λ2λ1=560nm400nm=75

10n+5=14m+710n=14m+25n=7m+1

By inspection, for m1=2,n1=3 and m2=7,n2=10

Therefore, Δs=λ1D2d[(2n2+1)(2n+1)]
=400×109×12×0.1×103[(2×10+1)(2×3+1)]

=200×105(217)

Δs=2800×105=28mm
Hence, the distance between areas of total darkness will be 28mm

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