Question

Light of wavelength $5.0\times {10}^{-7}m$ falls on a pair of narrow slits separated by a distance $d$. The interference pattern on a screen placed $2.0m$ away shows that there is first dark fringe at the positions exactly opposite to each slit. The separation between the slits is:

• A. $0.5mm$
• B. $1mm$
• C. $2mm$
• D. $4mm$

Answer 1

The correct option is B $1mm$

We know that $\beta =\left(\frac{D\lambda }{d}\right)$
Here the distance between two dark fringes (fringe width) is equal to the separation between the slit, i.e.,
$y=\beta =\left(\frac{D\lambda }{d}\right)=d$
$\Rightarrow d=\frac{D\lambda }{d}$
$d^2=\lambda D\Rightarrow d=\sqrt{\lambda D}$
Or $d=(5.0\times {10}^{-7}\times 2.0{)}^{\frac{1}{2}}={10}^{-3}m=1mm$