Question

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

• A. 3250 $\stackrel{\circ }{A}$
• B. $6.5\times {10}^{-4}$
• C. 1.24 $\mu m$
• D. $2.6\times {10}^{-4}$

Answer 1

The correct option is C 1.24 $\mu m$

For first minima $\theta =\frac{\lambda }{a}$ or $a=\frac{\lambda }{\theta }$
$\therefore a=\frac{6500\times {10}^{-8}\times 6}{\pi }(As{30}^o=\frac{\pi }{6}radiant)$
$=1.24\times {10}^{-4}cm=1.24\mu m$