Question

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

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

Answer 1

The correct option is C 500 nm

From youngs double slit experiment we have

path difference $\left(\Delta x\right)=\frac{yd}{D}$

$y=1mm,d=0.5mmD=50cm=500mm$

So,

$\Delta x=\frac{1\times 0.5}{500}mm$

$\Delta x=\frac{0.5}{500}\times {10}^{6}nm$

$\Delta x=1000nm$

For the strongest intensity at $H$ there should be constructive interference

$\Rightarrow \Delta x=n\lambda$

where

$\lambda \Rightarrow$ wavelength of light

$n\to$ integer $(1,2,3,....)$

$1000=n\lambda$

For $n=1$

$\lambda =1000nm$

For $n=2$

$\lambda =\frac{1000}{2}=500nm$

For $n=3$

$\lambda =\frac{1000}{3}=333.3nm$

So,

For the visible light $\lambda =500nm$