Physics 6M
Lab #7:
The Interference of Light
1. Introduction
Thus far we have investigated the properties of waves in mechanical media, such as solids, liquids, and
gases. It should come as no surprise that light is a wavelike phenomenon, and that most of the properties of
mechanical waves have analogous representations with light. In particular, the principle of superposition
holds to very high accuracy;
1
and so the phenomena arising from the principle are easily demonstrated.
Experiment #1:
Young’s Double-Slit Experiment
When a light beam with well-defined wavelength (
i.e.
color) falls upon a pair of slits, the light that is
transmitted will exhibit a beautiful interference pattern, arising from the principle of superposition. If the
wavelength of light is
λ
and the spacing of the slits is
a
, then one will observe bright fringes at the angles
θ
m
given by the following formula:
sin(
m
)
=
m
a
m
=
0,
±
1,
±
2,
±
3,.
..
If
is a very small angle (much less than 1 radian), then we can use the small-angle approximation:
sin(
)
≈
tan(
)
≈
and write simply
m
≈
m
a
m
=
0,
±
1,
±
2,
±
3,.
..
(Note that in order to use the small-angle approximation,
must be measured in radians, not degrees.)
Ordinarily one observes the y-coordinate of the interference maximum on a screen; the
y
-coordinate of the
maximum is given by
If we project these light waves onto a distant screen (where the distance
L
from the slits to the screen is far
greater than the separation
a
between the slits) then (again using the small-angle approximation) we can
find the physical distance
y
on the screen between the center of the pattern and bright fringe #
m
:
y
m
=
L
tan
−
1
m
≅
L
m
a
m
=
0,
±
1,
±
2,
±
3,.
..
This formula tells us that there will always be a maximum at y = 0; this is because for
y
= 0 the path lengths
for the rays emerging from each slit will be identical; hence there will be constructive interference.
Experiment: