Question

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 _____ $\times 10^{-5} m$.

Answer 1

$a \sin \theta=\frac{3 \lambda}{2}$
$\frac{y}{L}=\theta=\frac{3 \lambda}{2 a}$
$y_{1}=\frac{3 \lambda_{1} L}{2 a}$
$y_{2}=\frac{3 \lambda_{2} L}{2 a}$
$L =2 \,m$
$\lambda_{2}=655 \,nm$
$\lambda_{1}=650\, nm$
$a =0.5\, nm$
$\Delta y = y _{2}- y _{1}=\frac{3\left(\lambda_{2}-\lambda_{1}\right)}{2 a } L$
$=\frac{3(655-650)}{2 \times 0.5 \times 10^{-3}} \times 2 \times 10^{-9}$
$=\frac{3 \times 5 \times 2}{1 \times 10^{-3}} \times 10^{-9}$
$=3 \times 10^{-5}$