Q. In Young’s double slit experiment, when violet light of wavelength 4358 $\mathring{\mathrm{A}}$ is used, the 84 fringe are seen in the field of view, but when sodium light of certain wavelength is used, then 62 fringes are seen in the field of view, the wavelength of sodium light is
A) 6893 $\mathring{\mathrm{A}}$
B) 5904 $\mathring{\mathrm{A}}$
C) 5523 $\mathring{\mathrm{A}}$
D) 6429 $\mathring{\mathrm{A}}$
Explanation
(b) As field of view is same in both cases
$n_{1}\beta_{1} = n_{2}\beta_{2}$
Or $n_{1}\left( \frac{D\lambda_{1}}{d} \right) = n_{2}\left( \frac{D\lambda_{2}}{d} \right)$
Or $\lambda_{2} = \left( \frac{n_{1}}{n_{2}} \right)\lambda_{1}$
$\therefore\ \ \lambda_{2} = \left( \frac{84}{62} \right) \times 4358$
$\lambda_{2} = 5904\ \mathring{\mathrm{A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.