Answer:
585 nm
Explanation:
The formula that gives the position of the m-th maximum (bright fringe) relative to the central maximum in the interference pattern produced by diffraction from double slit is:
[tex]y=\frac{m\lambda D}{d}[/tex][tex]\Delta y =\frac{m\lambda D}{d}[/tex]
where
m is the order of the maximum
[tex]\lambda[/tex] is the wavelength
D is the distance of the screen from the slits
d is the separation between the slits
The distance between two consecutive bright fringes therefore is given by:
[tex]\Delta y = \frac{(m+1)\lambda D}{d}-\frac{m\lambda D}{d}=\frac{\lambda D}{d}[/tex]
In this problem we have:
[tex]\Delta y = 3.9\cdot 10^{-4} m[/tex] (distance between two bright fringes)
D = 2.0 m (distance of the screen)
d = 3.0 x 10−3 m (separation between the slits)
Solving for [tex]\lambda[/tex], we find the wavelength:
[tex]\lambda=\frac{\Delta y d}{D}=\frac{(3.9\cdot 10^{-4})(3.0\cdot 10^{-3})}{2.0}=5.85\cdot 10^{-7} m = 585 nm[/tex]
