Question

A slit of width a is illuminated by red light of wavelength $6500\, \overset{\text{o}}{\mathop{\text{A}}}\,$ . If the first minimum falls at $\theta =30{}^\circ ,$ the value of $a$ is

• A. $6.5\times {{10}^{-4}}mm$
• B. $1.3\,\,micron$
• C. $3250\,\overset{\text{o}}{\mathop{\text{A}}}\,$
• D. $2.6\times {{10}^{-4}}cm$

Answer 1

Answer: (B)

$1.3\,\,micron$

Answer 2

According to principle of diffraction
$a\sin \theta =n\lambda$ where $n=$ order of secondary minimum $\therefore$
$a\sin 30{}^\circ =1\times (6500\times {{10}^{-10}})$
or $a=1.3\times {{10}^{-6}}m$ or $a=1.3\text{ }micron$