# Diffraction Of Light In Water

When light passes through an opening it is observed to spreadout. This is known as diffraction and becomes more pronouncedwith narrower openings.

Diffraction of light through wide and narrow openings

A similar effect also occurs when light hits an opaque edge, causingthe light to bend around the edge.

Diffraction of light around an edge

The fact that this happens is to be expected. Light is known tobe a wave and waves, such as water waves and sound waves, are also knownto expand through openings.
Water and sound waves are disturbances in flexible mediums. Such waves spread out because they contain areas of pressure within themedium, and regions of high pressure (wave-peaks) always expand intoregions of lesser pressure. But as far as we know, light doesn’ttravel though a medium so how can it spread out?

#### Huygens-Fresnel principle

The explanation of how light can spread is given by the Huygens-Fresnelprinciple. It states that every point on a wavefront can beconsidered a source for another wavefront which will then become asource for further wavefronts as shown:

Here we see a spherical wavefront generating a series ofwavelets. Each wavelet sits like a soap bubble atop a primarysoap bubble. The side parts of the wavelets are said tocombine and cancel each other, leaving behind only the front part ofthe wave.

#### Problems

This principle is used to predict what kinds of patterns will occurwhen light passes through different diffraction gratings such as singleand double slits. And while nobody denies that it does a goodjob of predicting, there are many problems in believing that thisrepresents a true model of what actually happens with light.
First, why would the wavelets be hemispheres rather than fullspheres? Shouldn’t nature produce full spheres rather thanhalf-spheres with edges?
Second, what happens to the original wavefront? Does it stopits forward motion, then generate the wavelets, and then cease toexist? And if it doesn’t stop its motion, wouldn’t itsvelocity (of c) be added to the wavelets making them move at2c? According to special relativity theory, light moves onlyat c, not more or less.
Third, why would the wavelets cancel each other on the side? There is no particular reason why they should as they are not ‘out ofphase’ with each other. This cancellation is just an assumptionrequired by the theory.
Fourth, if hemispherical wavelets were being produced, this would allowthe light to eventually turn back on itself as shown:

Here we see a primary wavefront, which generates a secondary wavelet,which generates a third/fourth/fifth, etc. Until finally we havea wave that flows backward. All light passing through empty spaceshould diffract and spread in all directions. Instead it diffractsonly when interacting with an opaque material.

#### The Edges

So how can diffraction work without a flexible medium, and why doesn’tlight diffract in empty space, as the Huygens-Fresnel principle wouldsuggest?
There is something being overlooked here. And that is theedges of the slit.
As light hits the slit, most of it either gets absorbed into the wallsor passes through the opening. But a small amount also hitsthe edges. What will happen to it?
If the material is reflective, light will bounce off in somedirection. Mostly though, the slit will be made of a darkmaterial. In that case the light might be reradiated from thatpoint via a different process, as described later. This diagramshows the idea:

Here we see light passing directly through the opening and a smallamount reradiated from the edges. The radiation from theedges will come out spherically and combine with the light passingstraight through. As a result it will produce interferencepatterns on a screen.

#### Single slit patterns

As evidence for this idea, consider this typical interference patternproduced by light passing through a single slit:

This pattern also fits with a prediction from the Huygens-Fresnelprinciple.
But there’s a major problem: a single slit shouldn’t produce aninterference pattern.
When a wave passes through a single slit, all that should happen isthat the sides of the flat wavefront that has been cut at either endwill expand in quarter circles as shown:

Since no waves crossover and interfere with each other, there’s noreason for any interference pattern to emerge.
This photograph shows what happens when water waves pass through asingle slit:

This was taken in a ripple tank. Plane waves come in from theleft, pass through an opening, and then emerge in a shape similar tothe previous diagram.
Notice there’s no interference pattern!
That fact that light produces an interference pattern indicateswe are dealing with multiple ‘sources’ and the additional lightsources are likely to be the slit’s edges.

#### Double slit patterns

What about double slits? Here’s a typical interferencepattern produced by light passing through two slits:

We have what looks like a large-scale pattern overlayed with asmall-scale pattern. This again fits with a prediction fromthe Huygens-Fresnel principle, but again doesn’t match a ‘normal’wave.
A wave passing through two slits should produce two widenedsemicircles like this:

When those semicircles overlap they will produce interference but thegap between interference peaks won’t be much different to thewavelength of the original wave.
A double slit water wave pattern looks like this:

The ‘screen’ shows only a large-scale interference pattern with nosecondary small-scale patterns on top. Given the shape of thewater emerging through the slits, there’s no conceivable way that asecondary pattern could appear.
So how can light produce a pattern within a pattern? Thereason is likely that we are dealing with four edges that generatefour radiation points as shown:

The pair of points belonging to each slit are close together and theseare what would be responsible for the small-scale pattern within thelarge-scale pattern.

#### The details

Let’s look now into the details of how the light-bending mightoccur. Earlier it was suggested that light was being absorbedand reradiated from the edges. But this seems unlikelybecause the amount of radiation would depend on how dark the materialwas, with fully dark materials (zero albedo) producing almost nodiffraction – and this is not what we observe.
Understanding how light interacts with edges requires understanding howlight can pass though solid materials like glass. We don’texactly understand this process, other than to say that light issomehow being absorbed by atoms on one side and reemitted on theother. This absorption/reemission process is going to requireinteraction with the electrons surrounding the atoms.
When the atoms are within a solid material, the electric fields fromthe electrons are going to be heavily overlapping each other on allsides. If the material is transparent, this allows light tomove directly though it in straight lines.

When the atoms are on the surface of a solid material, the fields fromthe electrons are going to be heavily overlapping each other on allsides but one. If the material is transparent and the lightwas coming from within at a low angle, this would allow the light to beinternally reflected, i.e. total internal reflection.

We don’t understand how light can be reflected in that manner butpresumably it has something to do with how the fields overlapdifferently at the surface.
Now what would happen if a group of atoms on the surface of a materialsuddenly came to an end?

The above diagram shows light skimming across the surface of a material. The light is moving within the material, but though the ‘cloud’of electrons belonging to the atoms in the top-most layer of thematerial. We will assume light is able do this even if thematerial is opaque as it is not actually passing though the material,i.e. it is not passing between the nuclei in the material.
Since the electron fields overlap each other, the light jumpsfrom one atom to the next. For the atom on the far right however,which corresponds to the edge of the material, its field overlaps onlyon its left side. How would light behave when it emerges on theother side of that atom? We don’t know, but it’s possible thatwhen light encounters this situation it radiates spherically as shown:

Such spherical radiation would then produce diffraction patterns ifcombined with other waves.

#### Conclusions

The way light diffracts is inconsistent with how other waveforms suchas water waves diffract. The reason why light producesinterference patterns is not due to the Huygens-Fresnel principle butmore likely has to do with how light interacts with the electric fieldsof atoms on the edges of diffraction gratings.

Suppose there is a dark room and through the window, there is a small hole. When light enters through tiny hole we see that through the small hole light enters but instead of just bright light, we. Wave Properties of Light Wave Properties of Light Important Vocabulary Reflection Refraction Diffraction What do you see? Mirage Occurs when a layer of hot air lies. Compare light scattering by small and large water droplets Clouds, fog and mist droplets are small enough that when light interacts with them its wave nature is significant. Light is not simply refracted or reflected at the drop surface. Of the microemulsion type “water in oil” (or reverse micelles). Processing of diffraction patterns of the synthesized nanoparticles of cadmium in water. Optical scheme spektrosensitometra ISP-73: 1 - source of light (incandescent tungsten ribbon lamp). Instead of a prism or diffraction P2 put prismatic.

We classically think of light as always traveling in straight lines, but when light waves pass near a barrier they tend to bend around that barrier and become spread out. Diffraction of light occurs when a light wave passes by a corner or through an opening or slit that is physically the approximate size of, or even smaller than that light's wavelength.

A very simple demonstration of diffraction can be conducted by holding your hand in front of a light source and slowly closing two fingers while observing the light transmitted between them. As the fingers approach each other and come very close together, you begin to see a series of dark lines parallel to the fingers. The parallel lines are actually diffraction patterns. This phenomenon can also occur when light is 'bent' around particles that are on the same order of magnitude as the wavelength of the light. A good example of this is the diffraction of sunlight by clouds that we often refer to as a silver lining, illustrated in Figure 1 with a beautiful sunset over the ocean.

We can often observe pastel shades of blue, pink, purple, and green in clouds that are generated when light is diffracted from water droplets in the clouds. The amount of diffraction depends on the wavelength of light, with shorter wavelengths being diffracted at a greater angle than longer ones (in effect, blue and violet light are diffracted at a higher angle than is red light). As a light wave traveling through the atmosphere encounters a droplet of water, as illustrated below, it is first refracted at the water:air interface, then it is reflected as it again encounters the interface. The beam, still traveling inside the water droplet, is once again refracted as it strikes the interface for a third time. This last interaction with the interface refracts the light back into the atmosphere, but it also diffracts a portion of the light as illustrated below. This diffraction element leads to a phenomenon known as Cellini's halo (also known as the Heiligenschein effect) where a bright ring of light surrounds the shadow of the observer's head.

The terms diffraction and scattering are often used interchangeably and are considered to be almost synonymous. Diffraction describes a specialized case of light scattering in which an object with regularly repeating features (such as a diffraction grating) produces an orderly diffraction of light in a diffraction pattern. In the real world most objects are very complex in shape and should be considered to be composed of many individual diffraction features that can collectively produce a random scattering of light.

One of the classic and most fundamental concepts involving diffraction is the single-slit optical diffraction experiment, first conducted in the early nineteenth century. When a light wave propagates through a slit (or aperture) the result depends upon the physical size of the aperture with respect to the wavelength of the incident beam. This is illustrated in Figure 3 assuming a coherent, monochromatic wave emitted from point source S, similar to light that would be produced by a laser, passes through aperture d and is diffracted, with the primary incident light beam landing at point P and the first secondary maxima occurring at point Q.

As shown in the left side of the figure, when the wavelength (λ) is much smaller than the aperture width (d), the wave simply travels onward in a straight line, just as it would if it were a particle or no aperture were present. However, when the wavelength exceeds the size of the aperture, we experience diffraction of the light according to the equation:

sinθ = λ/d

Where θ is the angle between the incident central propagation direction and the first minimum of the diffraction pattern. The experiment produces a bright central maximum which is flanked on both sides by secondary maxima, with the intensity of each succeeding secondary maximum decreasing as the distance from the center increases. Figure 4 illustrates this point with a plot of beam intensity versus diffraction radius. Note that the minima occurring between secondary maxima are located in multiples of π.

This experiment was first explained by Augustin Fresnel who, along with Thomas Young, produced important evidence confirming that light travels in waves. From the figures above, we see how a coherent, monochromatic light (in this example, laser illumination) emitted from point L is diffracted by aperture d. Fresnel assumed that the amplitude of the first order maxima at point Q (defined as εQ) would be given by the equation:

dεQ = α(A/r)f(χ)d

where A is the amplitude of the incident wave, r is the distance between d and Q, and f(χ) is a function of χ, an inclination factor introduced by Fresnel.

#### Diffraction of Light

Explore how a beam of light is diffracted when it passes through a narrow slit or aperture. Adjust the wavelength and aperture size and observe how this affects the diffraction intensity pattern.

Diffraction of light plays a paramount role in limiting the resolving power of any optical instrument (for example: cameras, binoculars, telescopes, microscopes, and the eye). The resolving power is the optical instrument's ability to produce separate images of two adjacent points. This is often determined by the quality of the lenses and mirrors in the instrument as well as the properties of the surrounding medium (usually air). The wave-like nature of light forces an ultimate limit to the resolving power of all optical instruments.

Our discussions of diffraction have used a slit as the aperture through which light is diffracted. However, all optical instruments have circular apertures, for example the pupil of an eye or the circular diaphragm and lenses of a microscope. Circular apertures produce diffraction patterns similar to those described above, except the pattern naturally exhibits a circular symmetry. Mathematical analysis of the diffraction patterns produced by a circular aperture is described by the equation:

sinθ(1) = 1.22(λ/d)

where θ(1) is the angular position of the first order diffraction minima (the first dark ring), λ is the wavelength of the incident light, d is the diameter of the aperture, and 1.22 is a constant. Under most circumstances, the angle θ(1) is very small so the approximation that the sin and tan of the angle are almost equal yields:

From these equations it becomes apparent that the central maximum is directly proportional to λ/d making this maximum more spread out for longer wavelengths and for smaller apertures. The secondary mimina of diffraction set a limit to the useful magnification of objective lenses in optical microscopy, due to inherent diffraction of light by these lenses. No matter how perfect the lens may be, the image of a point source of light produced by the lens is accompanied by secondary and higher order maxima. This could be eliminated only if the lens had an infinite diameter. Two objects separated by a distance less than θ(1) can not be resolved, no matter how high the power of magnification. While these equations were derived for the image of a point source of light an infinite distance from the aperture, it is a reasonable approximation of the resolving power of a microscope when d is substituted for the diameter of the objective lens.

Thus, if two objects reside a distance D apart from each other and are at a distance L from an observer, the angle (expressed in radians) between them is:

θ = D / L

## Diffraction Of Light In Water Energy

which leads us to be able to condense the last two equations to yield:

Where D(0) is the minimum separation distance between the objects that will allow them to be resolved. Using this equation, the human eye can resolve objects separated by a distance of 0.056 millimeters, however the photoreceptors in the retina are not quite close enough together to permit this degree of resolution, and 0.1 millimeters is a more realistic number under normal circumstances.

The resolving power of optical microscopes is determined by a number of factors including those discussed, but in the most ideal circumstances, this number is about 0.2 micrometers. This number must take into account optical alignment of the microscope, quality of the lenses, as well as the predominant wavelengths of light used to image the specimen. While it is often not necessary to calculate the exact resolving power of each objective (and would be a waste of time in most instances), it is important to understand the capabilities of the microscope lenses as they apply to the real world.

## Diffraction Of Light In Water Equation

#### Contributing Authors

Mortimer Abramowitz - Olympus America, Inc., Two Corporate Center Drive., Melville, New York, 11747.

## Diffraction Of Light Application

Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.