Two coherent monochromatic point S1 and S2 of wavelength λ=600 nm are placed symmetrically on either side of the center of the circle as shown. The sources are separate 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?

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The angular separation between two consecutive bright spots decreases as we move from p1 to p2 along the first quadrant

A dark spot will be formed at the point p2

The total number of fringes produced between p1 and p2 in the first quadrant is close to 3000

At P2 the order of the fringe will be maximum

answer is C.

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Detailed Solution

At P1 , △x=S1P1-S2P1=0 , so a bright fringe is formed.At P2 a bright spot with maximum order of the fringe is formed.△x=S1P2-S2P2=nλ ⇒d=nλ For bright fringe, n should be an integer. ⇒n=dλ=1.8×10-3600×10-9=3000 Take a point at angle θ from P2 . Path difference =dcos⁡θ=nλ⇒cos⁡θ=nλdDifferentating,⇒−sin⁡θdθ=(dn)λ⇒dθ=−(dn)λsin⁡θθ→ decreases ,sin⁡θ→ decreases dθ→ increases

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