Answer:
[tex]5.9\cdot 10^{-7}m[/tex]
Explanation:
The formula to calculate the position of the m-th maximum in the interference pattern produced by the diffraction of light from a double slit is
[tex]y_m=\frac{m \lambda D}{d}[/tex]
where
y is the distance of the maximum from the central bright fringe
m is the order of the maximum
[tex]\lambda[/tex] is the wavelength of the light
D is the distance of the screen from the slits
d is the distance between the slits
Here we have:
[tex]d=3.0\cdot 10^{-3} m[/tex] (distance between slits)
D = 2.0 m (distance of the screen)
[tex]y=3.9\cdot 10^{-4} m[/tex] is the distance of the 1st maximum after the central maximum from the central fringe (therefore, taking m = 1)
Solving for [tex]\lambda[/tex], we find the wavelength:
[tex]\lambda=\frac{yd}{mD}=\frac{(3.9\cdot 10^{-4})(3.0\cdot 10^{-3})}{(1)(2.0)}=5.9\cdot 10^{-7}m[/tex]
