# 41. A double slit arrangement produces interierence for sodium light $(\lambda=589 nm )$ that have an angular would the angular separation be $10 \%$ greater? (1) $527 nm$ (2) $648 nm$ (3) $722 nm$ (4) $449 nm$

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41. A double slit arrangement produces interierence for sodium light $(\lambda=589 nm )$ that have an angular would the angular separation be $10 \%$ greater? (1) $527 nm$ (2) $648 nm$ (3) $722 nm$ (4) $449 nm$

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The angular positions of the maxima of a two-slit interference pattern are given by
dsinθ=mλ, where d is the slit separation, λ is the wavelength, and m is an integer.
If θ is small, sinθ may be approximated by θ in radians.
Then, θ=mλd to good approximation.
The angular separation of two adjacent maxima is Δθ=λ/d.
Let λ' be the wavelength for which the angular separation is greater by 10.0%.
Then, 1.10λ/d=λ/d or
λ′ =1.10λ=1.10(589nm)=648nm