example #$1$: Double slit interference

a double slit interefeernece pattern is created by two narrow slits spaced $0\mathrm{.}2$ mm apart. The distance between the first and fifth maxima on a screen $60$ cm behind the slits is $6$ mm$.$

$1.$ Set up the mathematical condition for the first order maximum on the viewing screen.

$2.$ Set up the mathematical condition for the fifth order maximum on the viewing screen.

$3.$ Recall that ym $=$Ltanthetam $=$ Lmlambda$/$d$.$ Express delta y $=$ y$5-$y$1$ algebraically.

$4.$ Determine the wavelength of the light used in this experiment in nm$.$