Answer:
[tex]1.152\ \mu m[/tex]
[tex]1.44\ \mu m[/tex]
Explanation:
d = Gap between slits = 0.142 mm
[tex]\lambda[/tex] = Wavelength of light = 576 nm
L = Distance between light and screen = 3.5 m
m = Order = 2
Difference in path length is given by
[tex]\delta=dsin\theta=m\lambda\\\Rightarrow \delta=2\times 576\times 10^{-9}\\\Rightarrow \delta=0.000001152\ m\\\Rightarrow \delta=1.152\times 10^{-6}\ m=1.152\ \mu m[/tex]
The difference in path lengths is [tex]1.152\ \mu m[/tex]
For dark fringe the difference in path length is given by
[tex]\delta=(m+\dfrac{1}{2})\lambda\\\Rightarrow \delta=(2+\dfrac{1}{2})\times 576\times 10^{-9}\\\Rightarrow \delta=0.00000144\ m=1.44\ \mu m[/tex]
The difference in path length is [tex]1.44\ \mu m[/tex]
