Question

Two slits separated by a distance of $1mm$ are illuminated with red light of wavelength $6.5\times {10}^{-7}m$. The interference fringes are observed on a screen placed $1m$ from the slits. The distance between the third dark fringe and the fifth bright fringe is equal to

• A. $0.65mm$
• B. $1.625mm$
• C. $3.25mm$
• D. $0.975mm$

Answer 1

The correct option is B $1.625mm$


Distance of 5th bright fringe from the centre $=5\beta$
Distance of 3rd dark fringe from the centre $=2\beta +0.5\beta =2.5\beta$

Therefore, distance between 5th bright fringe and 3rd dark fringe $\Delta y=5\beta -2.5\beta =2.5\beta$
$=2.5\frac{\lambda D}{d}=\frac{2.5\times 6.5\times {10}^{-7}\times 1}{{10}^{-3}}$
$=1.625\times {10}^{-3}m=1.625mm$