Diffraction is the bending of radiation (such as light) around the edge
of an obstacle or by a narrow aperture. Diffraction results from the interference
of light waves that pass an opaque body, producing a fuzzy region
between the shadow area and the lighted area that, upon close examination,
is actually a series of light and dark lines. A diffraction grating contains
many fine, parallel slits or scratches (about 12,000 per cm or 30,000 per
in.) and disperses light into its colors. These gratings are used in diffracting
spectroscopes.
Wave properties of light can be understood with the help of two
very general
principles (Babinet's and Huygens'). Both principles will explain the
distribution of light obtained by shining coherent light on a screen through
the opening of an otherwise coherent plate.
We will shine parallel light through openings of arbitrary number and shape and observe the pattern of interfering light (a screen pattern). Since the plate is opaque, there is no light wave immediately behind it. Just behind any opening of the plate, the light is the same as it would have been without a plate.
Babinet’s Principle
This principle
compares the screen patterns of complementary plates. Complementary
plates 1 and 2 are such that plate 1 has openings where plate 2 is opaque
and vice versa. In order to relate the screen patterns of plate 1
and plate 2, we imagine a plate 3 which is obtained by combining openings
of plate 1 and plate 2. Plate 3 transfers light where either plate
1 or 2 would. In the setup to the left the lens focuses
parallel light onto
the screen. The pattern on the screen is the geometrical-optics
image of the light source. We can think of the overall
darkness as a result
of the sum of two waves,
one from openings of plate 1 and the other from openings in
plate 2.
In this point of view, the darkness, which is present almost everywhere,
is due to the destructive interference of the waves from the two
complementary
plates. For such darkness to exist, the two waves must be out of
phase and have the same amplitude at each point on the screen. This
result is called Babinet’s principle:
the screen patterns due to complementary plates are the same,
except for the geometrical-optics image of the light source.
Let us use Babinet’s principle to find what occurs when light passes through a small aperture in a plate. Plate 1 is a plate with a single small hole at center. Plate 2, the complement of plate 1, is open everywhere except for a very small opaque region at the center (dot). In the same setup as above most of light wave passes through plate 2 undisturbed, and forms an image on the screen as if the small central dot was not even on the plate. But since the dot is opaque, it must absorb some of the energy from the light wave. The absorbed energy results in oscillating charges, which in turn give off electromagnetic waves in all directions. This leads us to believe that the dot emits waves in all directions which can be seen on the screen in addition to the source image. This is why the dot's shadow is not completely black. Now we consider plate 1, with the small hole in the middle. By Babinet’s principle, the screen pattern, due to the plate with the tiny hole, should be the opposite of the one with the dot. Therefore the central hole must emit a wave in all directions. Now we have demonstrated that a small illuminated hole acts as a point source.
Huygens' Principle
Using the idea that light is a wave, Huygens was able to explain the mechanism
for propagation of light. He believed that light propagates from
a source like a wave on the water surface. Every point on the wavefront
of a light wave generates a secondary spherical wavelet. This means
that a light wave can be approximated by a sufficient number of point
sources of light.
We have just observed that a wave coming out of a hole looks like one
from a point source. Huygens' principle says that the waves coming
through holes of any arbitrary plate look just like those coming from
a large collection of coherent, small sources of light located where the
holes are.