Question

In a double-slit experiment the distance between slits is 5.0 mm and the slits are 1.4 m from the screen. Two interference patterns can be seen on the screen: one due to light of wavelength 460 nm, and the other due to light of wavelength 650 nm. What is the separation in meters on the screen between the m = 2 bright fringes of the two interference patterns?

Answer 1

Step-by-step explanation:

It is given that,

Distance between the slits, d = 5 mm = 0.005 m

Distance between slit and screen, D = 1.4 m

For m = 2, and
`\lambda_1=460\ nm=460* 10^(-9)\ m`

`x_1=(m\lambda_1 D)/(d)`

`x_1=(2* 460* 10^(-9)* 1.4)/(0.005)`

`x_1=0.0002576\ m`

For m = 2, and
`\lambda_2=650\ nm=650* 10^(-9)\ m`

`x_2=(m\lambda_2 D)/(d)`

`x_2=(2* 650* 10^(-9)* 1.4)/(0.005)`

`x_2=0.000364\ m`

Separation between two fringes is :

`\Delta x=x_2-x_1`

`\Delta x=0.000364-0.0002576`

`\Delta x=0.0001064`

`\Delta x=1.064* 10^(-4)\ m`

Hence, this is the required solution.