# The wave nature of light

Hello,

In a double slit experiment the slit separation is 2.0mm and two wavelengths 750nm and 900nm illuminate the slits. A screen placed 2m from the slits. at what distance from the central maximum on the screen will a bright fringe from one pattern first conincide with a bright fringe from the other?

my formula?
d = sin[the] / (m [lamb]

Thanks!
Dx

at what distance from the central maximum on the screen will a bright fringe from one pattern first conincide with a bright fringe from the other?
d=2E-3meters, &lambda;1=750E-9m, &lambda;2=900E-9m, D=2m (D being adjacent leg of right triangle, y1 and y2 being opposite legs, &theta; being angle between slits.)
y1 = m&lambda;1D / d = (1)(750E-9m)(2m)/(2E-3)m = 7.5E-4m
y2 = n&lambda;2D / d = (1)(900E-9m)(2m)/(2E-3)m = 9.0E-4m
were n=m=1, WHICH THEY're not.
You can't solve it trigonometrically.
In order to solve it, you need to equate
y1=y2=m&lambda;1D/d = n&lambda;2D/d
Then you just solve for m:
m = (&lambda;2/&lambda;1)n = 1.2n
The first instance of this relation being true is if m=6 and n=5
Now you just solve y1 and y2 above to get...

y1=y2=0.0045m