Question

In Young's double slit experiment, when violet light of wavelength $4358\mathring{A}$ is used, the $84$ fringes 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. $6893\mathring{A}$
• B. $5904\mathring{A}$
• C. $5523\mathring{A}$
• D. $6429\mathring{A}$

Answer 1

Answer: (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 ${\lambda }_2=\left(\frac{n_1}{n_2}\right){\lambda }_1$
$\therefore {\lambda }_2=\left(\frac{84}{62}\right)\times 4358$
${\lambda }_2=5904\mathring{A}$