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

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 $\lambda_1=460\ nm=460\times 10^{-9}\ m$

$x_1=\dfrac{m\lambda_1 D}{d}$

$x_1=\dfrac{2\times 460\times 10^{-9}\times 1.4}{0.005}$

$x_1=0.0002576\ m$

For m = 2, and $\lambda_2=650\ nm=650\times 10^{-9}\ m$

$x_2=\dfrac{m\lambda_2 D}{d}$

$x_2=\dfrac{2\times 650\times 10^{-9}\times 1.4}{0.005}$

$x_2=0.000364\ m$

Separation between two fringes is :

$\Delta x=x_2-x_1$

$\Delta x=0.000364-0.0002576$

$\Delta x=0.0001064$

$\Delta x=1.064\times 10^{-4}\ m$

Hence, this is the required solution.