Answer:
515 nm
Explanation:
The equation that gives the position of the maxima (bright fringes) in the interference pattern produced on a distant screen by the diffraction of light through two slits is
[tex]y=\frac{m\lambda D}{d}[/tex]
where
y is the distance of the maximum (bright fringe) from the central maximum
m is the order of the maximum
[tex]\lambda[/tex] is the wavelength of the light used
D is the distance of the screen
d is the separation between the slits
In this problem we have:
[tex]d=0.5 mm = 0.5\cdot 10^{-3} m[/tex] is the separation between the slits
D = 3.30 m is the distance of the screen
m = 1 (we are analyzing the 1st bright fringe)
[tex]y=3.40 mm = 3.40\cdot 10^{-3} m[/tex] is the distance of the 1st bright fringe from the central maximum
Solving for [tex]\lambda[/tex], we find the wavelength of the light used:
[tex]\lambda=\frac{yd}{mD}=\frac{(3.40\cdot 10^{-3})(0.5\cdot 10^{-3})}{(1)(3.30)}=5.15\cdot 10^{-7} m = 515 nm[/tex]
