Question

The two slits are 1 mm 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

Answer 1

Answer: (C)

Given $\lambda =5\times 10^{-7}$ m, $D$ = 1 m, $d$ = 1 mm.
Distance of $n^{th}$ bright fringe from the centre
$=\frac{nD\lambda }{d}$
where $n=1,2,\mathrm{3.....}$
So the distance of 5th bright fringe = $\frac{5D\lambda }{d}$
Distance of $n^{th}$ dark fringe from the centre
$=\left(n-\frac{1}{2}\right)\frac{D\lambda }{d}$
where $n=1,2,3,4$
$3^{rd}$ dark fringe = $\left(3-\frac{1}{2}\right)\frac{D\lambda }{d}=\frac{5}{2}\frac{D\lambda }{d}$
$=\frac{5\times 1\times 5\times 10^{-7}}{2\times 1\times 10^{-3}}=12.5\times 10^{-4}m=1.25mm$