Double-slit Experiment

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.
!
!
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If d < < L then the difference in path length r1 - r2 travelled by the two
rays is approximately:
r1 - r2 dsin
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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,….
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The condition for destructive interference is r1-r2 = (m+0.5)
,m=1,2,…
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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,…
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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)
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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
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