Question

Two sources are placed on x- axis at a separation $d=3\lambda$. An observer starts moving from A on a circular track of radius $R(R>>d)$. How many bright points and dark points will he observe? Find the angular positions of maxima and minima.

• A. Total No. of bright spots and dark spots are 12.
• B. Total No. of bright spots and dark spots are 3.
• C. Angular position of maxima is $\frac{\pi r}{6}$.
• D. Angular position of minima is $\frac{\pi r}{12}$.

Answer 1

Answer: (A), (C), (D)

The correct options are
A Total No. of bright spots and dark spots are 12.
C Angular position of maxima is $\frac{\pi r}{6}$.
D Angular position of minima is $\frac{\pi r}{12}$.

let's take some assumptions,
1- All sources are coherent.
2- At $B$ maxima, $n=0$
3-At $C$ maxima, $n=3$

Total no. of maxima in the first quadrant=3, and no. of minimas=3
Hence, In a full circle,
Total no. of maxima=12
Total no. of minimas=12

Calculation of angular position:
$dsin\theta =n\lambda$
$d(sin{\theta }_1-sin{\theta }_2)=n\lambda sin{\theta }_1-sin{\theta }_2=\frac{\lambda }{d}$
given, $R>>>d$
so, ${\theta }_1-{\theta }_2=\frac{\lambda }{d}$


then, the bright fringe width $\left(\theta \right)$ = $\frac{\pi r}{2\times 3}=\frac{\pi r}{6}$
for dark fringe $\left(\theta \right)=\frac{\pi r}{12}$

so, option A, C and D are correct.