Question

32. In Young’s double slit experiment , when violet light of wavelength 435.8nm is

used, then 84 fringes are seen in the field of view, but when sodium light of a

certain wavelength is used, 62 fringes are seen in the field of view, calculate the

wavelength of sodium light :​

Answer 1

we know, number of fringes = length of region/fringe width

also we know, fringe width, $\beta=\frac{\lambda D}{d}$

where D is distance between slit and screen , d is seperation between slits and $\lambda$is wavelength of monochromatic light is used in YDSE.

so, number of fringes = $\frac{d\times\textbf{length of region}}{\lambda D}$

here it is clear that number of fringes is inversely proportional to wavelength of monochromatic light.

so, $\frac{N_1}{N_2}=\frac{\lambda_2}{\lambda_1}$

given, $N_1=84,\lambda_1=435.8nm,N_2=62$

applying above derived formula,

$\frac{84}{62}=\frac{\lambda_2}{435.8}$

or, $\lambda_2=\frac{84\times435.8}{62}=590.4381nm$

hence, answer should be 590.4381nm