Two slits S₁ and S₂ , arranged symmetrically around the central line, are illuminated by monochromatic light having wavelength . The slit separation is d . Light transmitted by these slits falls onto a screen ₁ placed at a distance D from the slits. Slit S₃ is positioned exactly at the central line, and slit S₄ is at a distance z from S₃ . A second screen ₂ is situated an additional distance D away from ₁ . Find the

Step-by-step solution

Let the intensity of light from each of the slits S₁ and S₂ be I₀ . The intensity at a point on screen ₁ at a distance y from the central line is given by: I(y) = 4I₀ ^2 ( d y D ) For slit S₃ , positioned at the central line ( y = 0 ), the intensity is: I₃ = 4I₀ ^2(0) = 4I₀ For slit S₄ , positioned at y = z = D 4d , the phase difference is: = 2 d D ( D 4d ) = 2 The intensity at S₄ is: I₄ = 4I₀ ^2 ( 4 ) = 2I₀ Slits S₃ and S₄ act as coherent secondary sources for the screen ₂ . The maximum and minimum intensities on