Two coherent monochromatic point sources S 1 and S 2 of wavelength λ = 600 n m are placed symmetrically on…

Two coherent monochromatic point sources S1 and S2 of wavelength λ=600nm are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance d=1.8 mm. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is Δθ . Which of the following options is/are correct?

  1. A dark spot will be formed at the point P2
  2. The angular separation between two consecutive bright spots decreases as we move from P1 to P2 along the first quadrant
  3. At P2 the order of the fringe will be maximum
  4. The total number of fringes produced between P1 and P2 in the first quadrant is close to 3000

Solution

At point P2;

Δx=d=1.8 mm=3000 λ

Hence a (bright fringe) will be formed at P2

Now   Δx=d cos⁡θ=nλ

cos⁡θ=nλd, θ is with the x-axis.

-sinθ Δθ=Δnλd

Δθ=-Δn λd sin⁡θ

Δθ increases as θ decreases

At   P2,  the order of fringe will be maximum.

For total no. of bright fringes d=nλ  ⇒  n=3000

∴   total no. of fringes =3000

Asked in: JEE Advanced 2017 (Paper 2)

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