Question

Light of wavelength $5.0\times {10}^{-7}m$ falls on a pair of narrow slits separated by a distance 2d. The interference pattern on a screen placed 2.0 m away shows that there is first dark fringe at the positions exactly opposite to each slit. The separation between the slits is:

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

Answer 1

The correct option is B. 1 mm

We know that, fringe width $\beta =\left(\frac{D\lambda }{2d}\right)$

Here the distance between two dark fringes in equal to the separation between the slit, i.e.,
$2d=\frac{D\lambda }{2d}$

or $d^2=\frac{\lambda D}{4}$

or $d=\sqrt{\frac{\lambda D}{4}}$
Or $d=(\frac{5.0\times {10}^{-7}\times 2.0}{4}{)}^{\frac{1}{2}}=0.5\times {10}^{-3}m=0.5mm$.

Therefore the separation between the slits is 2d = 1 mm.