Sodium light of wavelengths \(650\, nm\) and \(655\, nm\) is used to study diffraction at a single slit of aperture \(0.5\, mm\). The distance between the slit and the screen is \(2.0 \,m\). The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is \(\times 10^{-5} \,m\)

\(\frac{ y }{ L }=\theta=\frac{3 \lambda}{2 a } \quad L =2 m\)

\(y _{1}=\frac{3 \lambda_{1} L }{2 a } \quad \lambda_{2}=655\, nm\)

\(y _{2}=\frac{3 \lambda_{2} L }{2 a } \quad \lambda_{1}=650\, nm\)

\(a=0.5 \,nm\)

\(\Delta y = y _{2}- y _{1}=\frac{3\left(\lambda_{2}-\lambda_{1}\right)}{2 a } L\)

\(=\frac{3(655-650)}{2 \times 0.5 \times 10^{-3}} \times 2 \times 10^{-9}\)

\(=\frac{3 \times 5 \times 2}{1 \times 10^{-3}} \times 10^{-9}\)

\(=3 \times 10^{-5}\)