Question

A slit of width $a$ is illuminated by a monochromatic light of wavelength $650nm$. The value of $a$ when the first minima falls at an angle of diffraction of ${30}^0$ is

• A. $1.3\times {10}^{-6}m$
• B. $2.6\times {10}^{-6}m$
• C. $3.9\times {10}^{-6}m$
• D. $5.2\times {10}^{-6}m$

Answer 1

The correct option is A $1.3\times {10}^{-6}m$

$\frac{x}{D}=sin\theta =\frac{\lambda }{a}$
$sin{30}^0=\frac{650\times {10}^{-9}}{a}$
$a=\frac{650\times {10}^{-9}}{sin{30}^0}$
$=\frac{650\times {10}^{-9}}{1/2}(\because sin{30}^0=1/2)$
$=1.3\times {10}^{-6}m$