JEE Advanced 2017 · Paper 2 · Physics Q11

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PhysicsMultiple correct+4 / -2Question 11 of 54

Two coherent monochromatic point sources $S_1$ and $S_2$ of wavelength $\lambda = 600$ nm 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 $\Delta\theta$ . Which of the following options is/are correct?

A circle with horizontal and vertical diameters; P₁ at the top and P₂ at the right end of the horizontal diameter. Sources S₁ and S₂ lie on the horizontal diameter symmetrically about the centre, a distance d apart. Two close radii in the first quadrant mark the angular separation Δθ.

A dark spot will be formed at the point

P_2

P_2

the order of the fringe will be maximum

The total number of fringes produced between

P_1

and

P_2

in the first quadrant is close to 3000

The angular separation between two consecutive bright spots decreases as we move from

P_1

P_2

along the first quadrant

Answer and worked solution

Official answer: B, C

Path difference. At a point on the circle at angle $\phi$ from $P_1$ (far-field approximation, since the circle is much larger than $d$ ), the path difference is $d\sin\phi$ .

At $P_2$ ( $\phi=90^\circ$ ) it is $d=1.8\text{ mm}$ , so the order is $\dfrac d\lambda=\dfrac{1.8\times10^{-3}}{600\times10^{-9}}=3000$ . That is an integer, so $P_2$ is bright, and it is the highest order. (A) is false; (B) is true.
First quadrant. The order runs from 0 at $P_1$ to 3000 at $P_2$ : about 3000 fringes. (C) is true.
Spacing. $d\cos\phi\,\Delta\phi=\lambda$ gives $\Delta\phi=\dfrac\lambda{d\cos\phi}$ , which increases towards $P_2$ . (D) is false.

(B), (C)

Topics:Interference and Young's double slit

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JEE Advanced 2017 · Paper 2, Physics question 11