Page 425 - Schaum's Outline of Theory and Problems of Applied Physics

410 PHYSICAL AND QUANTUM OPTICS [CHAP. 33

SOLVED PROBLEM 33.2
When two trains of waves meet on the surface of a body of water, the resulting interference pattern is
obvious. However, when the light beams from two flashlights overlap on a screen, there is no evidence of
an interference pattern. Why not? Is there any way in which the interference of light can be demonstrated?

There are two reasons why such an experiment does not yield a conspicuous interference pattern. First, the
wavelengths found in light are so short that such a pattern would be on an extremely small scale. Second (and more
important), all sources of light (except lasers) emit light waves as short trains of random phase and not as continuous
trains. The interference that occurs between light beams from two independent sources is therefore averaged during
all but the briefest of observation times and cannot be seen by eye or recorded on photographic film. Such light
sources are said to be incoherent.
To exhibit an interference pattern in light, sources must be used whose waves have fixed phase relationships
during the observation period. The waves from one source can be in step with those from the other when they
are produced, or out of step, or something in between, but the essential thing is that the relationship be constant.
Such sources are coherent. In Fig. 33-2 the radio waves from an antenna are coherent, whereas the light waves
from an ordinary lamp of any kind (except a laser) are incoherent. Three ways to construct coherent sources are as
follows:

1. Pass light from a single source (such as an illuminated slit or a narrow filament) through two or more other slits.
The waves that emerge from the latter slits are necessarily coordinated and can interfere to produce a visible
pattern.
2. Combine a direct light beam from a source with an indirect beam from the same source produced by refraction
or reflection. This is how the interference patterns produced by thin oil films floating on water are caused.
3. Coordinate the radiating atoms in each individual source so that the radiating atoms always emit wave trains in
step with one another. This is done in the laser.

Coherent radio
waves

Incoherent light
waves
Fig. 33-2. (From Modern Technical Physics, 6th Ed., Arthur Beiser, c 1992. Reprinted by permission of Pearson
Education, Inc.)

SOLVED PROBLEM 33.3
Describe the nature and origin of the interference pattern produced by light that comes from a single slit
and then passes through a double slit.
In Fig. 33-3(a) the slits A and B are illuminated by light from the slit S, so the wave trains from A and B

are coherent. Figure 33-3(b) shows how the wave trains interfere constructively on the screen at S and D, and
destructively at C. Constructive and destructive interference alternate on the screen to produce a pattern of parallel
light and dark lines.

SOLVED PROBLEM 33.4
When two light beams of the same wavelength interfere, the result is a pattern of bright and dark lines.
What becomes of the energy of the light waves whose destructive interference leads to the dark lines?

The missing energy is found in the bright lines, whose brightness is greater than the simple addition of the two
light beams would produce without interference. The total energy remains the same.