Question

A slit of width $a$ is illuminated by white light for red light $(\lambda =6500\stackrel{o}{A})$, the first minima is obtained at $\theta ={30}^o$. Then the value of $a$ will be:

• A. $3250\stackrel{o}{A}$
• B. $6.5\times {10}^{-4}nm$
• C. $1.24$ microns
• D. $2.6\times {10}^{-4}cm$

Answer 1

The correct option is C $1.24$ microns

For first minima $\theta =\frac{\lambda }{a}$ or $a=\frac{\lambda }{\theta }$
$\therefore a=\frac{6500\times {10}^{-8}\times 6}{\pi }\left(As{30}^o=\frac{\pi }{6}radian\right)$
$=1.24\times {10}^{-4}cm$
$=1.24$microns.