Question

In a double slit experiment, the separation between the slits is $1\text{mm}$, the wavelength of light used is $5\times {10}^{-7}\text{m}$ and the distance of the screen from the slits is $1\text{m}$. How many bright fringes are formed in one centimeter width, on the screen?

• A. $20$
• B. $25$
• C. $30$
• D. $40$

Answer 1

The correct option is A $20$

Given:
$d=1\text{mm}=1\times {10}^{-3}\text{m}$
$\lambda =5\times {10}^{-7}\text{m}$
$D=1\text{m}$

Now, fringe width is given by,
$\beta =\frac{\lambda D}{d}=\frac{5\times {10}^{-7}\times 1}{1\times {10}^{-3}}=5\times {10}^{-4}\text{m}$

$\Rightarrow \beta =5\times {10}^{-2}\text{cm}$

Therefore, number of bright fringes formed in $1\text{cm}$ width,
$n=\frac{1}{\beta }=\frac{1}{5\times {10}^{-2}}=20$

Hence, $\left(A\right)$ is the correct answer.

Why this question ? The distance between two successive bright bands is equal to $\beta$. So, within a distance of '$\beta$', there'll be one bright band. Similarly, within a distance of '2$\beta$', there'll be two bright bands, and so on. Let there're $n$ bright bands in a distance of $x$, so that, $x=n\beta$. Therefore, in general we can write that number of bright fringes formed in a width $x$ of the screen is equal to $\frac{x}{\beta }$. Here, both $x\text{and}\beta$ must be in the same units.