Q. The two slits are $1mm$ apart from each other and illuminated with a light of wavelength $5 \times 10^{- 7}m$. If the distance of the screen is $1\ m$ from the slits, then the distance between third dark fringe and fifth bright fringe is
A) $1.5\ mm$
B) $0.75\ mm$
C) $1.25\ mm$
D) $0.625\ mm$
Explanation
(c) Distance of 5$^{th}$ bright fringe from central fringe,
$X_{5B} = \frac{5\lambda D}{d}$ …(i)
Distance of 3$^{rd}$ dark fringe from central fringe,
$X_{3D} = \frac{(2 \times 3 - 1)\lambda D}{2d} = \frac{5}{2}\frac{\lambda D}{d}\ \ \ \ldots(ii)$
From (i) and (ii) required distance
$X_{5B} - X_{3D} = \left( 5 - \frac{5}{2} \right)\frac{\lambda D}{d} = \frac{5}{2} \times \frac{5 \times 10^{- 7} \times 1}{1 \times 10^{- 3}} = 1.25\ mm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.