Two slits S₁ and S₂ , located symmetrically about the central axis, are illuminated by monochromatic light of wavelength . The distance between these slits is d . The light transmitted through the slits strikes a screen ₁ positioned at a distance D from them. A slit S₃ is located on the central axis, while another slit S₄ is at a distance z from S₃ . An additional screen ₂ is placed a further distance D from ₁ . Calc

Step-by-step solution

The path difference for the light waves from slits S₁ and S₂ reaching a point on screen ₁ at a distance y from the central axis is given by: x = y d D The intensity at any point on ₁ is: I = I₀ ^2 ( x ) where I₀ is the maximum intensity on ₁ . For slit S₃ , which is on the central axis ( y = 0 ): x₃ = 0 I₃ = I₀ ^2(0) = I₀ For slit S₄ , which is at a distance y = z = D d from the central axis: x₄ = z d D = ( D d ) d D = I₄ = I₀ ^2 ( ) = I₀ ^2( ) = I₀ Since I₃ = I₄ , the slits S₃ and S₄ act as coherent secondary sour