Question

A slit of width a is illuminated by white light. For red light ($\lambda =6200\stackrel{\circ }{A}$), the first minima is obtained at a diffraction angle of ${30}^{\circ }$. then the value of a is

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

Answer 1

The correct option is C $1.24$ micron

For first minima
$a\sin \theta =\lambda$
$\therefore a=\frac{\lambda }{{\sin \theta }_1}=\frac{6200\times {10}^{-10}}{{\sin 30}^{\circ }}=1.24\times {10}^{-6}m$
$=1.24u$