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

Answer: 2

Width of central maxima, $w=\frac{2D\lambda }{a}$
width of central maxima is directly proportional to the wavelength
$\frac{w_2}{w_1}=\frac{{\lambda }_2}{{\lambda }_1}$
$\frac{w_2}{w_1}=\frac{{\lambda }_2}{{\lambda }_1}{w}_2=\frac{0.70}{0.42}\times 2=3.37cm=337\times 10^{-2}cm$