Question

A single slit of width $0.14\text{mm}$ is illuminated normally by monochromatic light and diffraction bands are observed on a screen $2\text{m}$ away. If the centre of the second dark band is $1.6\text{cm}$ from the middle of the central bright band, the wavelength of light used.

• A. $5000\mathring{A}$
• B. $2000\mathring{A}$
• C. $5600\mathring{A}$
• D. $4000\mathring{A}$

Answer 1

The correct option is C $5600\mathring{A}$

Given, $a=0.14\text{mm};D=2\text{m};y=1.6\text{cm}$

In single slit diffraction, the condition for minima is,

$a\sin \theta =n\lambda$

Here, $\sin \theta =\frac{y}{D}$

$\therefore \frac{ay}{D}=n\lambda$

$\Rightarrow \lambda =\frac{ay}{Dn}$

Substituting the data gives,

$\lambda =\frac{1.6\times {10}^{-2}\times 0.14\times {10}^{-3}}{2\times 2}[\because n=2]$

$=5.6\times {10}^{-7}\text{m}=5600\mathring{A}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.