In an interference of light experiment, coherent light that contains two wavelengths: 640 nm (red-orange) and 425 nm (indigo-blue), passes through two narrow slits separated by 5.35 μm, and the interference pattern is observed on an observation screen 2.51 m away. (1 μm = 1×10-6 m, 1 nm = 1×10-9 m.)

Question

What is the linear separation on the screen between the third bright fringes produced by the two wavelengths on one side of the central bright fringe in the experiment?  (in meters)
 
Note:  There is no need to make a small angle approximation here: you can calculate what you need directly.

Answer 1

Thiiiis question.
Okay, so the only two formulas you need are:
1) dsinθ=mλ
2) y=Ltanθ

You already have all of your variables:
d=5.35x10^-6m
m=3
L=2.51m
λ_blue=4.25x10^-7m
λ_red=6.40x10^-7m

So now, just sub your values into formula 1 to find θ_blue and θ_red, (13.78727427... degrees for blue, and 21.03133713... degrees for red).

From there, just sub your θ_blue and θ_red into formula 2 to find your y_blue and y_red, and then find the difference between the two.

In the end, I think your linear separation should come to something like: 0.3491501095m...I think.