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 $99$

Let the length of the screen on which the fringes are obtained be $L_0$.

Thus the fringe width if 92 fringes are obtained is $\frac{L_0}{92}$.

We know that fringe width $=\frac{D\lambda }{d}$

Hence, for new wavelength ${\lambda }^{\prime }$, let there be n fringes.

Thus $\frac{D{\lambda }^{\prime }}{d}=\frac{L_0}{n}$

Thus $n=92\frac{\lambda }{{\lambda }^{\prime }}=99$