Question

in the young's double slit experiment the slits are 0.2mm apart and the screen is 1.5m away . it is observed that distance between the central bright and fourth dark fringe is 1.8cm. find the wave length of light used

Answer 1

hope it will help you

Answer 2

Answer:

Wavelength of the light used = $6.857\times 10^{-7}\ \rm m.$

Explanation:

Given:

• Separation between the slits, $\rm d = 0.2\ mm = 0.2\times 10^{-3}\ m.$
• Distance between the screen and the slits, $\rm D = 1.5\ m.$
• Distance between the central bright fringe and the fourth dark fringe, $\rm y_4 = 1.8\ cm = 1.8\times 10^{-2}\ m.$

We know,

In the double-slit experiment, the position of the $\rm m^{th}$ bright fringe from the center of the central fringe is given by

$\rm Y_m = \dfrac{m\lambda D}{d}.$

And the position of the $\rm m^{th}$ dark fringe from the center of the central fringe is given by

$\rm y_m = \left(m- \dfrac{1}{2}\right ) \dfrac{\lambda D}{d}.$

where $\lambda$ is the wavelength of the light used.

For the fourth dark fringe, m = 4, the position of this fringe from the central bright fringe is given by

$\rm y_4=\left ( 4-\dfrac 12\right )\dfrac{\lambda D}{d}=\dfrac 72 \dfrac{\lambda D}{d}\\\\\Rightarrow \lambda =\dfrac{y_4\times 2d}{7 D}\\\\Putting\ all\ the\ values,\\\\\lambda = \dfrac{(1.8\times 10^{-2})\times2\times 0.2\times 10^{-3} }{7\times 1.5}=6.857\times 10^{-7}\ m.$

It is the required wavelength of the light used.