Question

In Young's double slit experiment using sodium light $(\lambda =5898\mathring{A}),$ $92$ fringes are seen. If given colour $(\lambda =5461\mathring{A}),$ is used, how many fringes will be seen:

• A. $62$
• B. $67$
• C. $85$
• D. $99$

Answer 1

The correct option is D $99$

In youngs double slit experiment

$n=$ no. of fringes, $\lambda =$ wavelength

$x=\frac{n\lambda D}{d}$

we are given $n_1=92$, ${\lambda }_1=58.98\mathring{A}$

$n_2=?$, ${\lambda }_2=5461\mathring{A}$

$n_1{\lambda }_1\left(\frac{D}{d}\right)=n_2{\lambda }_2\left(\frac{D}{d}\right)$

$\Rightarrow n_1{\lambda }_1=n_2{\lambda }_2$

$92\times 5898=n_{2}5461$

$n_2=99$