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Wave Optics

Question
CBSEENPH12039957

On the first minimum adjacent to the central maximum of a single slit diffraction pattern, the phase  difference between the Huygens wavelet from the edge of the slit and the wavelet from the midpoint of the slit is

  • π/4 radian
  • π/2 radian
  • π radian
  • π/8 radian

Solution

C.

π radian

For the first minima at P, a sin θ = nλ


where , N = 1
rightwards double arrow space straight a space sin space straight theta space equals space straight lambda
so space phase space difference comma
increment straight ϕ subscript 1 space equals space fraction numerator increment straight x subscript 1 over denominator straight lambda end fraction space straight x space 2 straight pi space equals space fraction numerator left parenthesis straight a divided by 2 right parenthesis space sin space straight theta over denominator straight lambda end fraction space straight x space 2 straight pi

equals space minus space fraction numerator straight lambda over denominator 2 straight lambda end fraction space straight x space 2 straight pi space equals space straight pi space rad

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