Question

The two slits at a distance of 1 mm are illuminated by the light of wavelength $6.5\times {10}^{-7}m$. The interference fringes are observed on a screen placed at a distance of 1 m. The distance between third dark fringe and fifth bright fringe will be:

• A. 0.65 cm
• B. 4.8 mm
• C. 1.62 mm
• D. 3.25 cm

Answer 1

The correct option is C 1.62 mm

For dark Fringe,

$x=\frac{(2n-1)\lambda D}{2d}$
$X_3=\frac{(2\times 3-1)\times 6.5\times {10}^{-7}m\times 1m}{2\times {10}^{-3}m}$

$x_3=1.63\times {10}^{-3}m$
For bright Fringe

$x=\frac{n\lambda D}{d}$

$\therefore X_5=\frac{5\times 6.5\times {10}^{}-7m\times 1m}{{10}^{-3}m}$

$x_5=3.25\times {10}^{-3}m$
Distance between third dark fringe and fifth bright fringe = $(x_5-x_3)=1.62mm$