need help on my hw problem

Question

A green fringe produced by double slit interference lies 2 cm from the center of a screen placed 1 m from the double slit. If the screen is moved back so that it is now a distance of 4 m from the double slit,

(a) How far from the center of the screen will this green fringe lie?

Answer 1

Use the formula y=mDλ/d where y=distance from the center of the screen, m is the order number, D=the distance the screen is from the two slits and d is the slit separation. For this problem y= .02 cm when D=1 m. Then y₁/D₁ = .02 m /1 m =mλ/d. Now y₂ =mλD₂/d = .02m• 4m /1m and so y₂= .08 m = 8 cm.