devarshi-dt-logo

Question:

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=1.8mm. 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?

At P2 the order of the fringe will be maximum

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

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

A dark spot will be formed at the point P2

Solution:

Given d=1.8×10⁻³m and λ=6×10⁻⁷m
Path difference at point P Δx=S1P−S2P=dsinθ where θ angle is measured from vertical line as shown in figure.
For bright fringe dsinθ=mλ ——— 1
Point P1 is the point of central maxima.
At point P2, path difference (Δx)=d
If P2 is the point of the fringe, then d=mλ ⇒m=d/λ=3000
On differentiating equation (1) dcosθ(Δθ)=(Δm)λ= constant for consecutive bright fringe.
cosθ↓ ⇒ Δθ↑ as θ varies from 0 to π/2
Hence A and C are correct answer.