Question

In Young’s double slit experiment the separation of the slits is 1.9 mm and a screen situated at a distance of 1 meter from the slits. If five dark fringes are 1.25 mm apart, calculate the wavelength of the light.

Answer 1

Given:

In Young’s double slit experiment the separation of the slits is 1.9 mm and a screen situated at a distance of 1 meter from the slits. Five dark fringes are 1.25 mm apart.

To find:

Wavelength of light used in YDSE.

Calculation:

Distance of the 5th dark fringe is 1.25 mm.

$\therefore \: \dfrac{ (2n + 1)\lambda D}{2d} = y$

$= > \: \dfrac{ \{(2 \times 5)+ 1 \}\lambda D}{2d} = 1.25$

$= > \: \dfrac{ \{11 \}\lambda D}{2d} = 1.25$

$= > \: \dfrac{ \{11 \}\lambda \times 1000}{2 \times 1.9} = 1.25$

$= > 11000 \lambda = 4.75$

$= > \: \lambda = \dfrac{4.75}{11000}$

$= > \: \lambda = 0.43 \times {10}^{ - 3} \: mm$

$= > \: \lambda = 43 \times {10}^{ - 5} \: mm$

$= > \: \lambda = 430 \times {10}^{ - 6} \: mm$

$= > \: \lambda = 430 \: \mu m$

So , final answer is :

$\boxed{ \sf{ \large{ \red{ \: \lambda = 430 \: \mu m}}}}$