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{n D \lambda}{d}$
where $n = 1 , 2 , 3 .....$
So the distance of 5th bright fringe = $\frac{5 D \lambda}{d}$
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 = 1.25 \, mm$