Two coherent sources separated by distance d are radiating in pha… - Vidyadip

MCQ

Two coherent sources separated by distance $d$ are radiating in phase having wavelength $\lambda$. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of $n=4$ interference maxima is given as

✓
(a) $\sin ^{-1} \frac{n \lambda}{d}$
B
(b) $\cos ^{-1} \frac{4 \lambda}{d}$
C
(c) $\tan ^{-1} \frac{d}{4 \lambda}$
D
(d) $\cos ^{-1} \frac{\lambda}{4 d}$

✓

Answer

Correct option: A.

(a) $\sin ^{-1} \frac{n \lambda}{d}$

(a) $I_0=R^2=\frac{R_2^2}{4}$
Number of $H P Z$ covered by the disc at $b=25 cm$
$n_1 b_1=n_2 b_2 \\n_2=\frac{n_1 b_1}{b_2}+\frac{1 \times 1}{0.25}=4$
Hence the intensity at this point is
$I=R^{\prime 2}=\left(\frac{ R _5}{2}\right)^2$
$=\left(\frac{R_5}{R_4} \times \frac{R_4}{R_3} \times \frac{R_3}{R_2}\right)^2 \times\left(\frac{R_2}{2}\right)^2$ or $1=[0.9]^6$$I_1=0.531 I_0$
Hence the correct answer will be (a).

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