Question

In the setup shown in the figure $(D>>d)$ and $d=4\lambda$. Find the total number of maxima on the screen.

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is C $7$

Since, $D>>d$
Path difference,
$\Delta x=d\cos \theta$
$(\Delta x{)}_{min}=0$ for $\theta ={90}^{\circ }$
$(\Delta x{)}_{max}=d$ for $\theta =0^{\circ }$
But $d=4\lambda$
$\therefore (\Delta x{)}_{max}=4\lambda$ at point $O$.

For maxima :
$\Delta x=4\lambda ,3\lambda ,2\lambda ,\lambda$
Note : - $\Delta x=0$ can not be consider because angle $\theta ={90}^{\circ }$can not be achieved.

Similarly, maximas will also form on the lower half of the screen.
So, total maxima will be due to,
$\Delta x=4\lambda ,\Delta x=3\lambda \left(\text{both side}\right),\Delta x=2\lambda \left(\text{both side}\right),\Delta x=\lambda \left(\text{both side}\right)$

So, $n=7$

Why this question? Caution : Observe that here the path difference is $d\cos \theta$ not $d\sin \theta$. Carefully observe the difference in YDSE setup for both the cases.