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# A slit of width 'a' is illuminated by white light. For what value of 'a' will the first minimum for red light of wavelength $\lambda =650 \;nm$ appear for $\theta =30^{\circ}$?

$(a)\;6.5 \times 10^{-7}\;m \\ (b)\;1.3 \times 10^{-7}\;m \\ (c)\;6.5 \times 10^{-6}\;m \\ (d)\;1.3 \times 10^{-6}\;m$

Can you answer this question?

1st order minima condition is
$a \sin \theta =m \lambda$
Where m is order of minima $m=1$
$a =\large\frac{m \lambda }{\sin 30}$
$\qquad=\large\frac{1 \times 650 \times 10^{-10}}{1/2}$$m$
$\qquad= 1.300 \times 10^{-10}$
$\qquad= 1.3 \times 10^{-7}$
Hence b is the correct answer.
answered Jan 23, 2014 by