Optics 6 Question 32

34. Two coherent monochromatic point sources S1 and S2 of wavelength λ=600nm are placed symmetrically on either side of the centre of the circle as shown. The sources are separated by a distance d=1.8mm. 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?

(2017 Adv.)

(a) The angular separation between two consecutive bright spots decreases as we move from P1 to P2 along the first quadrant

(b) A dark spot will be formed at the point P2

(c) The total number of fringes produced between P1 and P2 in the first quadrant is close to 3000

(d) At P2 the order of the fringe will be maximum

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Solution:

 at P1Δx=0

at P2Δx=1.8mm=nλ

Number of maximas will be n=Δxλ=1.8mm600nm=3000

 at P2Δx=3000λ

Hence, bright fringe will be formed.

At P2,3000 th maxima is formed.

For (a) option

Δx=dsinθdΔx=dcosdθRλ=dcosθRdθRdθ=Rλdcosθ

As we move from P1 to P2

θcosθRdθ



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