# Double Slit Experiment - White Lite & Minimum Angular Displacement

1. Apr 23, 2012

### tnbstudent

1. The problem statement, all variables and given/known data

A two-component beam of light, consisting only of two wavelengths 650 nm and 520 nm, is used to obtain interference fringes in a double-slit experiment. The separation between the centers of the slits is 2.43×10−4 m and the distance of the plane of the slits from the screen is 720 cm. What is the smallest angular displacement from the central maximum where the centers of the bright fringes due to the two colors will coincide?

2. Relevant equations

sinθ=(m/d)λ
m is number of fringes
d is the width of the slit
sinθ=a/D
a is the distance from the center on the other side
D is the distance the slit is to the screen

λ1=650 nm
λ2 =520 nm
D=7.2 m
d= 2.43×10−4 m

3. The attempt at a solution
I set up a series of equations like this:
(m1/d)λ1 = (m2/d)λ2 = sinθ = a/D
(m1/2.43×10−4 m)*650nm = (m2/2.43×10−4 m)*520nm = a/7.2m
a=1.926*10^-2 *(m1) = 1.54*10^-2m* (m2)
I found that when m1 = 4 and m2 = 5, a =7.704*10^-2m
sinθ=a/d
sinθ=.0107
θ= .61°

Thanks for any help that will point me in the right direction