Question

In a sngle slit diffraction pattern the angular width of a central maxima is $30^{\circ}$ when the slit is illuminated by light of wavelength $6000\,\mathring{A}$. Then width of the slit will be approximately given as:

• A. $12 \times 10^{-6} m$
• B. $12 \times 10^{-7} m$
• C. $12 \times 10^{-8} m$
• D. $12 \times 10^{-9} m$

Answer 1

Answer: (B)

Angular width of central maxima in diffraction pattern is given as
$2 \theta=30^{\circ}$
Where we have
$\sin 30^{\circ}=\frac{\lambda}{b}$
$\Rightarrow b=\frac{\lambda}{\sin 30^{\circ}}=\frac{6000 \times 10^{-10}}{1 / 2}$
$=12000 \times 10^{-10} \,m$
$\Rightarrow b=12 \times 10^{-7} \,m$