diffraction pattern will be created on the screen. This pattern arises from interference
among light waves coming through different portions of the slit. We will assume that the
screen is far enough away from the slit that the rays that pass through are
approximately parallel to each other. This is called Fraunhofer diffraction. (Fresnel
diffraction occurs when the rays cannot be treated as parallel, and is discussed in more
advanced texts.)
The result of Fraunhofer diffraction is a pattern of light and dark bands (often called
fringes) on the screen, as shown above. The black-and-white image emphasizes the
light and dark pattern.
This pattern of light and dark can be explained using the concept of interfering waves.
As with double-slit interference, bright fringes result from constructive interference of
waves and dark fringes from destructive interference. The intensity of the bright fringes
diminishes the farther they are from the midpoint. The first bright fringe is located
straight across from the single slit. The other fringes are located in a symmetric pattern
on both sides of the center.
In the illustrations, we simplify the configuration necessary to produce the diffraction
pattern shown. A lens is typically used to focus the light, making the diffraction pattern
clearer.
To explain the source of the interference, we use Huygens’ principle and treat the light
passing through the slit as though it were made up of individual waves (wavelets)
emanating from a series of point sources, as shown in Concept 2. We focus on the
waves emanating from just two of those point sources to simplify the drawings and
explanations. As with double-slit interference, the difference in the waves’ path lengths
to the screen (and any resulting phase difference) determines whether they interfere
constructively, and create a bright fringe, or destructively, to create a dark fringe.
First, we show constructive interference. In Concept 3, we consider two waves from the
edges of the slit. They meet at the center of the screen. Since they travel the same
distance, there is no path length difference, which means they arrive in phase. Any
point source within the slit can be matched to a corresponding “mirror point” that is an
equal distance from the midpoint, but on the other side. The interference is completely
constructive, and the result is the central bright fringe, which is the brightest in the entire
diffraction pattern.
In Concept 4, we show how completely destructive interference creates a dark fringe. In
this case, we consider a wave on the left edge of the slit and a wave from the center of
the slit. The wave on the left travels one-half wavelength less to reach the screen than
the wave on its right. This means they will be completely out of phase when they meet
at the screen. In fact, every wave has a corresponding wave exactly half a slit away that
will cancel it at that screen location.
The regions between the lightest and darkest points are the result of intermediate
interference. In these regions, the overall interference is neither completely destructive
nor completely constructive, and the brightness at these points is between that of the
points just discussed.
Use Huygens' principle
Model light as emanating from point
sourcesConstructive interference
Causes bright fringes
Destructive interference
Causes dark fringes
34.8 - Resolving power
Resolving power: Ability to distinguish
between two objects.
Resolving power expresses the capability of an optical system to show the separation of
objects that are close together. This correlates to the instrument’s ability to show fine
detail. A microscope is one example of an instrument that needs a good deal of
resolving power. To be effective, a microscope must enable you to distinguish very
small, close details. Telescopes also must supply great resolving power to allow the
viewer to separate distant objects.
In concept 1 we show the importance of resolving power. The image of galaxy M100 on
the left was taken by the Hubble Space Telescope before a defect in its mirror was
corrected; the image on the right was taken after the defect was fixed. The right-hand
image shows much more detail, and many more distinct objects are visible due to the
greater resolving power achieved.
The Hubble telescope can resolve light sources that are less than 0.00003° (§ 0.0000005 rad) apart. What does that mean on a human
scale? It could resolve a pair of headlights roughly 3000 km away, approximately the distance from Denver to Miami. A great conceptual
design, some repairs and ongoing maintenance, and the fact that the telescope is above the blurring effects of the Earth’s atmosphere, all
Resolving power
Measures ability to distinguish between
two objects