Question

In Young's double slit experiment shown in figure. $S_1$ and $S_2$ are coherent souces and $S$ is the screen having a hole at a point $1.0mm$ away from the central line. White light ($400$ to $700nm$) is sent through the slits. Which wavelengths passing through the hole has strong intensity?

• A. $400nm$
• B. $700nm$
• C. $500nm$
• D. $667nm$

Answer 1

The correct option is C $500nm$

$y_n=\frac{n{\lambda }_{n}D}{d}$

$\Rightarrow {\lambda }_n=\frac{y_{n}d}{D}$

$when,n=1$

${\lambda }_1=\frac{y_{nd}}{D}=\frac{{10}^{-3}\times 0.5\times {10}^{-3}}{0.5}={10}^{-6}m=1000nm$

$1000$ $nm$ is not present in the range $400nm-700nm$

again$,$ where $n=2,$

${\lambda }_2=\frac{y_{n}d}{2D}=500nm$

Hence,

option $\left(C\right)$ is correct answer.