Question

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

Answer 1

Answer: 3

$a\sin \theta =\frac{3\lambda }{2}$
$\frac{y}{L}=\theta =\frac{3\lambda }{2a}$
$y_1=\frac{3{\lambda }_{1}L}{2a}$
$y_2=\frac{3{\lambda }_{2}L}{2a}$
$L=2m$
${\lambda }_2=655nm$
${\lambda }_1=650nm$
$a=0.5nm$
$\Delta y=y_2-y_1=\frac{3\left({\lambda }_2-{\lambda }_1\right)}{2a}L$
$=\frac{3(655-650)}{2\times 0.5\times 10^{-3}}\times 2\times 10^{-9}$
$=\frac{3\times 5\times 2}{1\times 10^{-3}}\times 10^{-9}$
$=3\times 10^{-5}$