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JEE Advanced Physics Wave Optics 2024 JEE Advanced 2024 (Paper 2)

JEE Advanced Physics Question (2024) — Solution

Question

Paragraph I: In a Young's double slit experiment, each of the two slits A and B, as shown in the figure, are oscillating about their fixed center and with a mean separation of 0.8 ~mm . The distance between the slits at time t is given by d=(0.8+0.04 t) mm , where =0.08 rad s ^ -1 . The distance of the screen from the slits is 1 ~m and the wavelength of the light used to illuminate the slits is 6000 Ã…. The interference pattern on the screen changes with time, while the central bright fringe (zeroth fringe) remains fixed at point O. The 8^ th bright fringe above the point O oscillates with time between two extreme positions. The separation between these two extreme positions, in micrometer ( m ), is ___________ .

Options

  1. A. A
  2. B. B
  3. C. C
  4. D. D

Answer

A. A

Step-by-step solution

aligned & y=n ( D d ) \\ & for 8^ th fringe \\ & y=8 D d \\ & y_ =8 D d_ \\ & y_ =8 D d_ \\ & y_ -y_ =8 D [ 1 d_ - 1 d_ ] \\ & =6000 Ã… aligned aligned & D =1 ~m \\ & ~d _ =0.34 ~mm \\ & ~d _ min =0.76 ~mm \\ & y_ -y_ =8 6000 10^ -10 1 [ 1 0.76 10^ -3 - 1 0.84 10^ -3 ] \\ & =8 6 10^ -4 [ 0.08 0.76 0.84 ]=601.5 m \\ & aligned (answer range is from 598 to 602 )

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