Question: Q. 10. Yellow light $(\lambda=6000 \AA)$ illuminates a single slit of width $1 \times 10^{-4} \mathrm{~m}$. Calculate : (i) the distance between the two dark lines on either side of the
central maxima, when the diffraction pattern is viewed on a screen kept $1.5 \mathrm{~m}$ away from the slit, (ii) the angular spread of the first diffraction minima.
A [O.D. Comptt. I, II, III 2012]
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Solution:
Ans. Separation between two dark bands on each side of central bright fringe $=$ width of bright fringe ,
We know width of the central fringe
$$ =\frac{2 D \lambda}{a} $$
where,
$D=$ distance of slit from screen,
$\lambda=$ wavelength of the light,
$a=$ width of the slit. $\quad 1 / 2$
According to question,
Width of central fringe $=\frac{1.5 \times 2 \times 6000 \times 10^{-10}}{1 \times 10^{-4}} \mathrm{~m}$
So the distance between the two dark lines on either side of the central maxima
Angular spread of the first diffraction minima
$$ \begin{aligned} & =\frac{\lambda}{a} \ & =\frac{6000 \times 10^{-10} \mathrm{~m}}{1 \times 10^{-4} \mathrm{~m}} \ & =6 \times 10^{-3} \mathrm{rad} \end{aligned} $$
