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In a Young's double slit experiment, the two interfering waves forming the interference pattern have the same amplitude. The phase difference between the two waves reaching a point X is 3 . What will be the phase difference between the two waves at a point Y if the intensity ratio at X and Y is 3: 2 ?

Options

  1. A4
  2. B3
  3. C2
  4. D6

Correct answer

C. 2

Step-by-step solution

The intensity I at any point in a Young's double slit experiment is given by I = 4I₀ ^2 ( 2 ) , where I₀ is the intensity of each individual wave and is the phase difference between the two interfering waves. Given the phase difference at point X is _X = 3 , the intensity at X is I_X = 4I₀ ^2 ( /3 2 ) = 4I₀ ^2 ( 6 ) = 4I₀ ( 3 2 )^2 = 4I₀ 3 4 = 3I₀ . Let the phase difference at point Y be _Y . The intensity at Y is I_Y = 4I₀ ^2 ( _Y 2 ) . The ratio of intensities is given as I_X I_Y = 3 2 . Substituting the expressi

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