Two coherent sources S and S are separated by a distance four tim… - Vidyadip

MCQ

Two coherent sources $S$ and $S$ are separated by a distance four times the wavelength $\lambda$ of the source. The sources lie along $y$ axis whereas a detector moves along $+x$ axis. Leaving the origin and far off points the number of points where maxima are observed is

A
(a) 2
✓
(b) 3
C
(c) 4
D
(d) 5

✓

Answer

Correct option: B.

(b) 3

(b)$I_A=R_1^2 $
$I_B=\left(R_1-R_2\right)^2=R_1^2\left(1-\frac{R_2}{R_1}\right)^2=R_1^2\left(1-\frac{3}{4}\right)^2=\frac{R_1^2}{16} $
$I_C=\left(R_1-R_2+R_3\right)^2=R_1^2\left(1-\frac{R_2}{R_1}+\frac{R_3}{R_1}\right)^2 $
$=R_1^2\left(1-\frac{R_2}{R_1}+\frac{R_3}{R_2} \times \frac{R_2}{R_1}\right)^2 \\=R_1^2\left(1-\frac{3}{4}+\frac{3}{4} \times \frac{3}{4}\right)^2=\left(\frac{13}{16}\right)^2 R_1^2=\frac{169}{256} R_1^2 $
$\therefore I_A: I_B: I_C=R_1^2: \frac{R_1^2}{16}: \frac{169}{256} R_1^2=256: 16: 169$

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