Diffraction

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Question

Light of wavelength 5 × 10^–7m is diffracted by an aperture of width 2 × 10^–3m. For what distance travelled by the diffracted beam does the spreading due to diffraction become greater than the width of the aperture?

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Solution

$\frac{\lambda }{a}D = a\$
Angular spread, $\theta=\lambda/d$
Linear spread $\theta D=\frac{\lambda D}{d}$
$\therefore \frac{\lambda}{d}\,D=d$
$\Rightarrow \,D=\frac{d^2}{\lambda}=\frac{(2\times10^{-3})^2}{5\times10^{-7}}\,m$
$= 8 \,m$

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