# Why does interference occur during diffraction?

## Diffraction and interference

Diffraction and interference phenomena do not occur very rarely, but are usually not taken into account.

Left picture: A steel ruler is held in front of the sun so that it completely covers it. In addition to the hidden sun, the edges of the ruler shine brightly. This phenomenon cannot be explained optically because there is no straight beam from the sun to the "eye" of the camera. Light is bent at the edge and thus reaches the lens. This is a consequence of the wave nature of light, waves always spread a little into the shadow area after an obstacle.
Middle and right: The same experiment can be carried out with the moon and easily observed without the risk of dazzling; Then the size comparison is also easy: the length of the light strips corresponds to the apparent diameter of the moon.

We are particularly interested in color phenomena that are created by superimposing the diffracted light waves.

### Light waves, coherent and incoherent light

Interference phenomena are proof of the wave nature of light. The following animated picture shows how the waves are superimposed during diffraction at a double slit. The gaps are assumed to be very narrow compared to the wavelength.
 Diffraction at the double slit: A plane wave runs from the left towards an absorbing screen with two small openings (gaps). You can see how constructive and destructive interference alternate in the waves running out to the right. When you move the mouse pointer over the image, the animation begins. To see the animation in a separate window, click HERE.
Huygens gave the vivid idea that every point of a wave surface can be imagined as the starting point of "daughter" waves, the superposition of which then results in the further advancing wave. In the picture above, the two openings in the aperture are the starting points for the secondary waves.
If one looks at gaps or openings whose width is greater than the wavelength, the phenomena become more complicated. In the forward direction, the waves emanating from the individual sections of the gap are superimposed constructively, but at a certain angle - even with a single gap - extinction occurs, but then the brightness increases again a little ... If you catch the light at a greater distance behind the gap on a screen, the following picture emerges:
 Diffraction at the slit. Above: monochromatic light, below: white light. Since the position of the light and dark stripes depends on the wavelength, the diffraction pattern is less clear with white light than with monochromatic light, and colors become visible.

A simple experiment: A fine hole is made in a piece of household aluminum foil with the tip of a sewing needle. Through this hole you can see a "point" light source, e.g. the reflection of the sun in a silver Christmas tree ball. (Don't be alarmed: in addition to the diffraction image shown below, you can also see the streaks in the glass body and lens of the eye. You may have to move the opening in front of the eye a little in order to be able to perceive the diffraction image.)
You can also use a camera instead of the eye: Diffraction pattern of a pinhole (pinprick in a household aluminum foil) with a diameter of approx. 0.04 mm, recorded with a digital camera. The light source was the low-voltage light bulb of a microscope light. Left: The exposure was chosen so that the brightest point is not yet overexposed. Right: The same with a longer exposure. The irregularities of the diffraction rings show that the needle prick did not create an exactly circular opening.
The calculation: Left: Sequence of colors when light is diffracted by a circular aperture. The scale below the spectrum shows the product of the aperture radius (in micrometers) times the deflection angle (in degrees). Right: The same with increased brightness. The then overexposed part (which cannot be displayed on the screen) was faded out in gray.
 Imagine, in the above simulation of diffraction at the double slit, one does not allow a uniform wave with straight fronts to come in from the left, but a mixture of waves from slightly different directions, without defined phase relationships among each other and with slightly different wavelengths. The left side would then look like a water surface when there is wind. On the right-hand side, the waves coming from the two openings would still overlap, but the mutual reinforcements or extinctions would take place in a completely random manner and alternating with time again and again somewhere else.In the case of an experiment with light, there would be no stripe image on the screen, but a diffuse light spot.

Such a wave mixture is called as described above incoherent. The incoherence of light from most light sources is the main reason that diffraction phenomena are usually not very clear. The sun's small angular expansion is enough to make many disappear. (Only recently has the laser become a convenient, bright light source with good coherence properties.)

Nevertheless, diffraction phenomena can also be observed in the wild. Colors, similar to those that appear in diffraction at the slit and at pinhole diaphragms (pictures above), are found in iridescent clouds:

Iridescent clouds. At a small angular distance from the sun, the delicate clouds shimmer dazzlingly bright in "mother-of-pearl" colors. The dark area above is blue sky. (You can find more pictures here.)

For comparison, the diffraction image of a circular diaphragm (see the images above) was superimposed on a light gray background. The brightness was chosen so high that the middle (up to about 13 units on the scale below) is outshone, so it should actually be much brighter. The scale below the picture indicates the aperture radius (in micrometers) times the deflection angle (in degrees).

Of course there are no pinholes floating in the sky. But there is a theorem (which only seems strange at first glance), which says that the diffraction patterns of opaque panes (outside the direct beam) match those of holes of the same shape and dimensions in an opaque aperture (theorem of Babinet). The water droplets in a cloud are not opaque, but for rough estimates you can in some cases ignore the light that has passed through. If the droplets are so small that the diffraction minimum occurs at an angular distance that is significantly larger than the angle at which the sun is seen (a little more than 0.5 °), then the finite size of the solar disk has little effect. However, colors can only be seen if the droplets are uniform in size in larger areas. If the droplets are all of the same size, the colors are seen in concentric circles and then speak of an aureole, especially if the appearance is caused by thin, barely visible clouds.

Left: courtyard and moderately colored ring around the sun. A black mirror (a glass pane painted black on the back) was used for the recordings. Right: The bluish aureole around the sun can be seen clearly, at a somewhat greater distance a delicate pink touch can be sensed more than seen. More pictures of it

In almost all of the many photos of aureoles and iridescent clouds that can be found on the Internet, the part closest to the sun is either covered or overexposed. The brightness is just too great there. Therefore, one rarely sees that the central part of the aureole is bluish.
If the cloud cover occasionally tears up in cloudy weather, then you can sometimes see the solar disk through a thinner part of the clouds without being dazzled. Such a moment is captured in the photo above right:

Warning: Looking directly into the sun or even in its vicinity can permanently damage your eyesight and must be avoided at all costs, even with sunglasses! A non-mirrored pane of glass is ideal for observing iridescent clouds and aureole from the sun. Hold the pane in such a way that the reflection of the sun cannot be seen.
 If the mist droplets are small and very uniform in size, the appearance can be quite colorful. Many impressive pictures can be found on the internet. Right: Aureole around the moon. Photo: Wiebke Salzmann. The center is overexposed. If you move the mouse pointer over the picture, the size of the moon disc is displayed in black. Sources: Wikimedia / Wikipedia, License CC BY-SA 3.0.
 It is therefore not absolutely necessary to have an opening in a diaphragm in order to produce visible diffraction phenomena. As an example on the left an aureole around the sun, caused by the curled fibers of a synthetic curtain fabric. The individual fibers are approx. 0.02 mm thick.
The iridescent clouds and aureoles around the sun or the moon come about essentially through diffraction of the light on the fog droplets. However, one is not dependent on approximations and estimates, because the scattering, refraction, diffraction and reflection of the light on the droplets can also be calculated exactly. How is shown elsewhere.

Another phenomenon based on reflection and diffraction, which one can occasionally see in the mountains or from an airplane, when one's own shadow falls on clouds or fog, is the glory around the counterpoint to the sun. In contrast to the phenomena treated so far, there is no simple, in particular no ray-optical explanation for this, only the poorly descriptive calculation of the Mie scatter.
Picture: Glorie, or the airplane ghost. Photo: "Brocken Inaglory" (site), source: Wikipedia, license CC BY-SA 3.0.

Dusty or tarnished (or faint) window panes, scratches in the glass, etc. can cause diffraction-based colors. Reflective surfaces should be mentioned in particular: a small, flat, reflective area on an otherwise matt or dark surface generates diffraction patterns in the reflected light, like an aperture in the transmitted light.

#### granulation

A rather inconspicuous, but everyday phenomenon: small, colorful dots appear on matt metal surfaces in the sunlight:

Goethe listed such phenomena quite completely in his color theory and described them as "epoptic", "catoptric" and "paroptric colors":
"373. If a polished silver is eaten away by separating water in such a way that the copper contained in it is dissolved and the surface becomes, as it were, rough, and the image of the sun is then reflected on the plate, it will shine back individually from each infinitely small raised point and the The surface of the plate appear in bright colors. Likewise, if you hold a black, unsmoothed paper in the sun and look carefully at it, you will see its smallest parts shining brightly in the most vivid colors. "

It has already been mentioned that laser light has much better coherence properties than sunlight. If you illuminate a matt surface, e.g. a sheet of paper, with a laser, the sheet does not appear evenly illuminated, but rather blotchy, "granulated". It's the same effect. But while this is seldom noticeable in sunlight, the granulation cannot be overlooked when illuminated with laser light and is sometimes perceived as annoying. Since the laser light is monochromatic, there are of course no additional colors.

Left: A sheet of white paper on which a triangle made of acrylic glass lies, illuminated with the light of a laser pointer that was fanned out a little by a magnifying glass attached in front of it. Width of the image section 11 mm. Right: The same gray coin as above, here in the laser light. The diameter of the coin is 21.2 mm. Unfortunately, the photos cannot reproduce the sparkle of the dots.

The pattern of spots is constant over time, but changes when the observer (or the light source or the object) moves. It is remarkable that the dots are always seen with the same sharpness, regardless of the distance to which the eye is set. Looked at through a magnifying glass, they don't get bigger, they get bigger.

The explanation of the effect is a little easier if one assumes that the eye or the camera is not focused on the observed area, so we will first examine this case. Under these conditions, light coming from a point will illuminate a small circular disk on the retina or film / sensor; Correspondingly, all light rays that meet at a point on the retina come from a small, approximately circular area of ​​the area under consideration. If this surface is illuminated with coherent laser light, then between the wave trains that come from different points there are fixed, time-constant phase relationships, and when the waves overlap in the image plane, then they can intensify, weaken or even extinguish, and whatever exactly happens depends on the fine details of the surface roughness. The area from which light strikes a point in the image plane is the larger, the wider the diaphragm is open. Smaller aperture leads to coarser granulation of the image, as can be seen in the following images:

 Granulation, left with aperture f: 3.5, right with aperture f: 8.

One could now think that the granulation would have to disappear if the focus is exactly on the observed object, because each point would then be mapped onto a point again. But this is only an idealization of ray optics: because of the wave nature of the light, there is no point in the focal plane as an image of a point, but a small light spot due to the limitation of the rays by the aperture. The light spots from neighboring image points overlap, and so there is again alternating amplification, weakening or extinction, granulation instead of uniform brightness.

The colorfulness of the dots on matt metal surfaces etc. in sunlight is due to the fact that the pattern of spots depends on the wavelength of the light. The wavelengths that we perceive in red create a different pattern than the ones seen in green, and the blue again a different one. So the overlay of all is then colorful.
You can think about this more precisely using a simplified example. Let us look at a small element, a flat micro-facet in the matt surface, which directs light to the eye. The light reflected from the facet fans out, the smaller the facet, the more, and if the facet is small enough, only part of the reflected (and diffracted) light passes through the pupil into the eye and is there on the retina focused. The sequence of colors from the center (of the "ray") outwards is very similar to that shown above for the case of a circular aperture. The colors that appear are shown again at the highest possible brightness on the screen. Depending on the perspective, the facet can show all of these colors.

In order for the dot pattern to arise, however, it is not necessary that flat facets are present. However, a detailed description of the diffraction effects that occur is neither useful nor feasible for any rough surface.

 Granulation can also be observed relatively often on thread-like objects: on cobwebs in the backlight, or, as in the picture on the left, on the hairs of plant seeds. This can be seen particularly well in photos when the image is somewhat blurred. Image: seed stand of dandelion, "blowball". Click to enlarge the image!

Even more Diffraction and interference phenomena can be found in the following sections about
Soap bubbles etc., about shimmering colors and about optical phenomena on spider webs.

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