Thomas Young's double slit experiment demonstrates the principles of interference effects in light waves. Light passing through two slits will produce interference patterns on a screen due to differences in the path lengths traveled by each wave. The conditions for constructive and destructive interference depend on the path length difference being equal to whole number or half-number multiples of the wavelength. Measuring the spacing of bright or dark bands allows the wavelength of monochromatic light to be calculated indirectly, even when the slit separation is much smaller than the screen distance.

1. Fei Hong 28450147
Example of Interference Effects in Light
Waves and Calculations
Thomas Young’s Double Slit Experiment
Two light rays pass through two slits, separated by a distance d and strike a screen
a distance, L.
!
!
!
If d < < L then the difference in path length r1 - r2 travelled by the two
rays is approximately:
r1 - r2 dsin
1

2. Fei Hong 28450147
Constructive and Destructive Interference
If two identical waves of wavelength start out in phase, travel at the
same speed for a distance of r1 and r2 respectively, where r1 r2 , the
crests of the one wave will be behind the crests of the other by a distance
of r1 - r2 .
The condition for constructive interference when the
waves recombine is r1 - r2 = m , m = 1,2,….
!
The condition for destructive interference is r1-r2 = (m+0.5)
,m=1,2,…
!
If the rays were in phase when they passed through the
slits, for constructive interference at the screen:
dsin = m , m = +/- 1, +/-2,...
For destructive interference at the screen:
dsin = (m +0.5 ) ,m =+/-1, +/-2,…
!
Interference Fringes
Bright bands- constructive interference
y B
m =
!
Dark bands- destructive interference
y Dm =
!
The space between darkspots
y = Note: for (indirectly) measuring the wavelength of light, if d L,
even when the wavelength of light is very small, the spacing between the
interference can still be large.
!
Sample problem (showing that measuring very short wavelengths using the
double slit experiment can be as accurate as when L/d is very large)
2

3. Fei Hong 28450147
Monochromatic light goes through two thin slits 0.02mm apart. It is found that the
second bright fringe on a screen 1.1 m away is 4.6 cm from the centre. What is the
wavelength of the light?
y2 = n (L/d)
where n = 2 ,
= dy2/2 = 0.02x10^-3m x4.6x10^-2/(2x 1.1m) = 4.2x 10- 7m = 420 nm
3