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 $5896\AA$, then the distance of 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 $0.047\text{cm}$

$\theta =\frac{\lambda }{a}$ ... (A)
$\theta =\frac{x}{f}$ ... (B)
From eqs. (A) and (B)
$\frac{\lambda }{a}=\frac{x}{f},x=\frac{f\lambda }{a}$ ... (C)
According to question $x=?,f=40\text{cm}$
$\lambda =5896\times {10}^{-8}\text{cm}$
$a=0.5\times {10}^{-1}\text{cm}$ ... (D)
From eqs. (C) and (D)
$x=\frac{40\times 5896\times {10}^{-8}}{5\times {10}^{-2}}=0.047\text{cm}$