Question

If two coherent source are placed at a distance of $3\lambda$ from each other symmetric to the centre of the circle as shown in the figure$(R>>\lambda )$, then the number of bright fringes produced on the screen placed along the circumference is :

• A. $16$
• B. $12$
• C. $8$
• D. $4$

Answer 1

The correct option is B $12$

The path diffrence between the two waves coming from $S_1$ and $S_2$ at $P$ and $Q$ is $3\lambda$. So here bright frings will form.


At $R$, path difference will be zero, since $S_{1}R=S_{2}R$.
So,


Bright fringes will form, when :
$\Delta x=0,\lambda ,2\lambda ,3\lambda$
as shown in the above diagram.
So,total number of bright fringes $=12$