Determine the angular separation between central maximum and firs… - Vidyadip

MCQ

Determine the angular separation between central maximum and first order maxima of the diffraction pattern due to a single slit of width $0.25\, mm$ when light of wavelength $5890\,\mathop A\limits^o $ is incident on it

✓
$3.534\times10^{-3}\, rad$
B
$2.35\times10^{-3}\, rad$
C
$1.47\times10^{-4}\, rad$
D
$15.8\times10^{-3}\, rad$

✓

Answer

Correct option: A.

$3.534\times10^{-3}\, rad$

a
$\sin \theta =\theta=\frac{\Delta}{\mathrm{a}}=\frac{(2 \mathrm{n}+1) \lambda}{2 \mathrm{a}}=\frac{3 \lambda}{2 \mathrm{a}} \quad(\because \mathrm{n}=1) $

$=\frac{3}{2} \times \frac{5890 \times 10^{-10}}{0.25 \times 10^{-3}}=3.534 \times 10^{-3} \mathrm{radian} $

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