In a double$-$slit experiment the distance between slits is $5\mathrm{.}9$ mm and the slits are $0\mathrm{.}82$ m from the screen. Two interference patterns can be seen on the screen: one due to light of wavelength $470$ nm $,$ and the other due to light of wavelength $590$ nm $.$ What is the separation in meters on the screen between the $m=2$ bright fringes of the two interference patterns?

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