Two coherent point sources S₁ and S₂ , vibrating in phase, emit light of wavelength . The distance separating the sources is 2 . Considering a line that passes through S₂ and is perpendicular to the line S₁ S₂ , find the smallest distance from S₂ at which an intensity minimum is found.

Step-by-step solution

Let the point of observation be P at a distance y from S₂ on the line perpendicular to S₁S₂ . The distance of P from S₁ is S₁P = d^2 + y^2 , where d = 2 is the distance between the sources. The path difference at P is given by: x = S₁P - S₂P = d^2 + y^2 - y For an intensity minimum (destructive interference), the path difference must be an odd multiple of 2 : x = (2n - 1) 2 At S₂ ( y = 0 ), the path difference is maximum and equals d = 2 . As y increases, the path difference x decreases. To find the smallest distan