Question

The two slits are 1mn apart from each of other and illuminated with a light of wavelength $5 \times 10^{- 7}m.$ If the distance of the screen is 1m from the slits, then the distance between third dark fringe and fifth bright fringe is:

• A. 1.2 mm
• B. 0.75 mm
• C. 1.25 mm
• D. 0.625 mm

Answer 1

Answer: (C)

1.25 mm

Answer 2

: Given : $\lambda = 5 \times 10^{- 7}m,D = 1m,d = 1mm$

Distance of $n^{th}$bright fringes from the centre$= \frac{nD\lambda}{d}$

Where n = 1,2,3……

So the distance of $5^{th}$bright fringes $= \frac{5D\lambda}{d}$

Distance of $n^{th}$dark fringe from the centre

$= \left( n - \frac{1}{2} \right)\frac{D\lambda}{d}$

Where n= 1,2,3……

$3^{rd}$dark fringe $= \left( 3 - \frac{1}{2} \right)\frac{D\lambda}{d} = \frac{5}{2}\frac{D\lambda}{d}$

Distance between them

$= \left( 5 - \frac{5}{2} \right)\frac{D\lambda}{d} = \frac{5}{2}\frac{D\lambda}{d}$

$= \frac{5 \times 1 \times 5 \times 10^{- 7}}{2 \times 1 \times 10^{- 3}} = 12.5 \times 10^{- 4}m = 1.25mm$