Question

A diffraction pattern is produced by a single slit of width $0.5\text{mm}$ with the help of a convex lens of focal length $40\text{cm}.$ If the wavelength of light used is $5896\mathring{\text{A}}$. The distance of the first dark fringe from the axis will be

• A. $0.047\text{cm}$
• B. $0.047\text{m}$
• C. $0.047\text{mm}$
• D. $47\text{cm}$

Answer 1

The correct option is A $0.047\text{cm}$

Given,

$a=0.5\text{mm};f=40\text{cm}\lambda =5896\mathring{A}$

The angular position of the diffraction pattern is given by,

$\theta =\frac{\lambda }{a}.......\left(1\right)$

Angular position also given by,

$\theta =\frac{x}{f}.......\left(2\right)$

From equation (1) and (2)

$\frac{\lambda }{a}=\frac{x}{f}$

$x=\frac{f\lambda }{a}$

$x=\frac{40\times {10}^{-2}\times 5896\times {10}^{-10}}{0.5\times {10}^{-3}}=0.047\text{cm}$

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