Rami Arieli: "The
Laser Adventure" Chapter 10 Section 0, page 2
Interference of Waves
In
Chapter
1 the basic properties of waves were explained.
In
section
1.2.3 the coherence property of laser radiation was briefly
explained.
Now, after explaining the properties of laser radiation from
many different aspects, a more comprehensive explanation can be given.
While studying physical optics, the conditions for
constructive and destructive interference between two beams, which come
from common origin, is explained:
-
Constructive Interference
- When the path difference between the two beams in an integral multiplication
of the wavelength. The result is brighter illumination
in these regions.
-
Destructive Interference
- When the path difference between the two beams in an odd multiplication
of half a wavelength. The result is dark bands
in these regions.
While deriving these theoretical conditions, the waves
are assumed to be perfect, and retain their shape over infinite distances.
In reality
the shape of a wave spread with distance, and after a distance of many
wavelengths, the conditions for interference are no longer fulfilled.
The problem is critical for light waves, because of the
very short wavelength.
As an example:
The wavelength of Helium-Neon laser is 0.6328 [mm]
(632.8 [nm]).
After advancing 1 meter from the light source, the wave advances
more than a million wavelengths (!).
If there is a deviation of 1 in a million in the laser frequency,
the deviation will cause a path difference of more than a wavelength, and
destroy the possibility to perform interference.