Q.
At the first minimum adjacent to the central maximum of a single-slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is
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a
π radian
b
π8 radian
c
π4 radian
d
π2radian
answer is A.
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Detailed Solution
The situation is shown in the figure. In figure A and B represent the edges of the slit AB of width a and C represents the midpoint of the slit. For the first minimum at P,For the first minimum at P,asinθ=λ . . . .(i) where λ is the wavelength of light. The path difference between the wavelets from A to C is Δx=a2sinθ=12(asinθ)=λ2 (using (i)) The corresponding phase difference Δϕ is Δϕ=2πλΔx=2πλ×λ2=π
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