Question

The diffraction pattern from a single slit is viewed on a screen. Using blue light of wavelength $0.42\mu m$ , the width of the central maximum is $2.0cm.$ If the width of the central maximum(in $cm$ ) when red light of wavelength $0.70\mu m$ is used is $337\times 10^{- x}$ find $x$ .

Answer 1

Width of central maxima, $w=\frac{2 D \lambda }{a}$
width of central maxima is directly proportional to the wavelength
$\frac{w_{2}}{w_{1}}=\frac{\lambda _{2}}{\lambda _{1}}$
$\frac{w_{2}}{w_{1}}=\frac{\lambda _{2}}{\lambda _{1}}w_{2}=\frac{0 . 70}{0 . 42}\times 2=3.37cm=337\times 10^{- 2 }cm$