Question

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) \( 449 nm \)

Answer 1

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