Question

In Young's double-slit experiment, how many maxima can be obtained on a screen (including the central maximum) on both sides of the central fringes if $\lambda =2000\stackrel{o}{A}$ and $d=7000\stackrel{o}{A}$

• A. $7$
• B. $12$
• C. $18$
• D. $4$

Answer 1

Answer: (A)

Let $n$ be the number of fringes on one side. Then,
$dsin\left(\theta \right)=n\lambda \Rightarrow sin\left(\theta \right)=\frac{n\lambda }{d}=\frac{n\times 2000}{7000}=\frac{n}{3.5}$
As we know,
$sin\left(\theta \right)\le 1\Rightarrow \frac{n}{3.5}\le 1\Rightarrow n\le 3.5$
Possible values of $n$ are $0,1,2\text{and}3$ .
So, total maxima are seven which includes one central bright, three above CB and three below CB on screen.