Question

The first diffraction minima due to a single slit diffraction is at $\theta ={30}^o$ for a light of wavelength 5000 $\mathring{A}$. The width of the slit is:

• A. $5\times {10}^{-5}cm$
• B. $10\times {10}^{-5}cm$
• C. $2.5\times {10}^{-5}cm$
• D. $1.25\times {10}^{-5}cm$

Answer 1

Answer: (B)

$10\times {10}^{-5}cm$

Condition for obtaining $m^{th}$ order minima is
$asin\theta =m\lambda$

Thus for obtaining first diffraction minima,

$asin\theta =\lambda$

$⟹a=\frac{\lambda }{sin\theta }$

$=\frac{5000\times {10}^{-10}m}{1/2}$

$=10\times {10}^{-5}cm$