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 [tex]\lambda_1=460\ nm=460\times 10^{-9}\ m[/tex]
[tex]x_1=\dfrac{m\lambda_1 D}{d}[/tex]
[tex]x_1=\dfrac{2\times 460\times 10^{-9}\times 1.4}{0.005}[/tex]
[tex]x_1=0.0002576\ m[/tex]
For m = 2, and [tex]\lambda_2=650\ nm=650\times 10^{-9}\ m[/tex]
[tex]x_2=\dfrac{m\lambda_2 D}{d}[/tex]
[tex]x_2=\dfrac{2\times 650\times 10^{-9}\times 1.4}{0.005}[/tex]
[tex]x_2=0.000364\ m[/tex]
Separation between two fringes is :
[tex]\Delta x=x_2-x_1[/tex]
[tex]\Delta x=0.000364-0.0002576[/tex]
[tex]\Delta x=0.0001064[/tex]
[tex]\Delta x=1.064\times 10^{-4}\ m[/tex]
Hence, this is the required solution.
