Light Scattering (Judy Jennings)

Quickwrite

Title: Phenomena of Rayleigh Scattering: Why is the Sky Blue? And Red?

Principle(s) Investigated: List all principles that apply to this activity.

Rayleigh Scattering, Tyndall Effect

Standards : CA- California K-12 Academic Content Standards

Subject: Science

Grade: Grade Seven

Area: Focus on Life Science

Area: Investigation and Experimentation

Sub-Strand 7: Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations. Students will:

Standard a.: Select and use appropriate tools and technology (including calculators, computers, balances, spring scales, microscopes, and binoculars) to perform tests, collect data, and display data.

Materials: Include a list of materials and sources from which they may be obtained.

Large clear container or glass

Flashlight

Water

Liquid skim milk

White paper

Procedure: Give a detailed explanation of the procedure and include diagrams if possible.

(http://www.exploratorium.edu/snacks/blue_sky/)

(15 minutes or less)

Fill the container with water. Place the light source so that the beam shines through the container. Add powdered milk a pinch at a time (OR liquid skim milk); stir until you can clearly see the beam shining through the liquid.

(15 minutes or more)

Look at the beam from the side of the tank and then from the end of the tank. You can also let the light project onto a white card, which you hold at the end of the tank. From the side, the beam looks bluish-white; from the end, it lo

Student prior knowledge: What prior concepts do students need to understand this activity?

Electromagnetic Radiation

(High Frequency, Short Wavelength) (Low Frequency, Long Wavelength)

*Remember, Low Frequency, Long Wavelength

Visible light spectrum

(Mnemonic to remember order, a person's name: Roy G. Biv)

This progression from left to right is from long wavelength to short wavelength, and from low frequency to high frequency light. The wavelengths are commonly expressed in nanometers (1 nm = 10^-9 m). The visible spectrum is roughly from 700 nm (red end) to 400 nm (violet end).

An example of white light, or close to white light, is the light from the sun. White light contains a continuous distribution of wavelengths.

(http://hyperphysics.phy-astr.gsu.edu/hbase/vision/specol.html#c2)

What is a nanometer?

A nanometer is one billionth of a meter.

1

1,000,000,00

Explanation:

Daytime Sky

The daytime sky's blue color is caused by the selective scattering of sun light by molecules in the air (our atmosphere contains mostly nitrogen and oxygen molecules). This selective scattering is called Rayleigh Scattering.

Why "Rayleigh?"

Lord Rayleigh

-English physicist

-Published (1871) "On the light

from the sky, its polarization and colour,"

Philosophical Magazine, series 4, vol.41

being the first to describe reasoning

behind the phenomenon of blue skies.

-Professor of Experimental Physics at

Cambrige University in 1879.

-Awarded the Noble Prize in Physics 1904

for "investigations of the densities of the

most important gases and for his

discovery of argon in connection

with these studies."

John William Strutt, Baron Rayleigh

Rayleigh Scattering describes the behavior of electromagnetic radiation (i.e. light) as it travels through a medium consisting of particles of size significantly smaller than its wavelength (The approximate diameter of air molecules are .3nm, approximately 1/1000 of the wavelength of light). It is considered selective because the degree to which a scattering effect by a molecule is achieved is dependent on the wavelength of incident light.

The underlying mechanism behind Rayleigh Scattering is the means by which a photon is absorbed and emitted by a particle smaller than the photon’s wavelength. A photon that encounters an atom (sufficiently sized for Rayleigh Scattering) will be absorbed by the electron cloud of that atom, causing the atom to oscillate. Almost immediately following absorption, the energy is released again in the form of another photon (with an energy and wavelength equal to the original photon) and radiated in any random direction from the atom (why random? I believe it has something to do with quantum mechanics). The net effect is that light approaching a group of these particles in one direction will be ‘scattered’ and sent in various random direction.

The mathematical formulae associated with Rayleigh Scattering state that the scattering effect described above more strongly affects higher frequency radiation (shorter wavelength) than lower frequency radiation (longer wavelength) as seen in the approximation below:

Scattering effect: (~λ−4) (where lambda equals wavelength)

Can also be written as: 1

λ4

Practice:

If the wavelengths in comparison were 2 and 4,

the scattering effect of wavelength 2 would be 16

times greater than that of wavelength 4.

2 1 = 1

(2)4 16

4 1 = 1

(4)4 256

A more advanced approach to the explanation of Rayleigh Scattering:

(http://www.itp.uni-hannover.de/~zawischa/ITP/scattering.html)

"Now look at a single "air particle", i.e. a nitrogen or an oxygen molecule. Fine details are not relevant now, we adopt a simple model of positive electric charge (containing almost all of the mass) surrounded by a cloud of negative charge. The dimension of this assembly is of the order of tenths of a nanometer, and thus several thousand times smaller than the wavelength of visible light.

If the molecule is exposed to an electric field, the centroids of the positive and the negative charges are somewhat pulled apart, the molecule becomes a minute electric dipole.

As the electrons have much smaller mass than the nuclei, the motion of the nuclei may be ignored at all, and the model for the molecule is reduced to a negatively charged small mass bound by some elastic force (of electrical origin) to an infinitely heavy nucleus.

If there is incident light with a certain wavelength and corresponding frequency, a periodic force acts on the elastically bound charge which induces forced oscillations. It is important that the frequencies of visible light are much smaller than the resonance frequencies of the molecules. From this one can conclude that the oscillation amplitudes are independent of the exciting frequency to a first approximation.

The molecule which we consider thus becomes an oscillating dipole, oscillating with the same frequency as the incoming wave, thus acts like a tiny antenna and emits electromagnetic radiation.

If the centroid of the negative charge −q is separated from that of the positive charge +q by a distance x₀, then the product q.x₀, which is called the dipole moment, is a suitable measure for the strength of the dipole (because the resulting field depends only on that quantity as long as the separation distance x₀ is very small compared to other relevant distances). For not too strong external fields, the dipole moment is proportional to the external field strength; the dipole moment divided by the field strength is called polarizability. The polarizability is the physical quantity characterizing the molecule which is relevant here, and which, for the cases of interest here, is almost independent of the frequency.

The calculation of the radiation emitted by an oscillating dipole can be found in textbooks on electromegnetism. The result is that the emitted radiative power is proportional to the square of the dipole moment and to the fourth power of the oscillation frequency. This is a consequence of the smallness of the dipole compared with the wavelength of the radiation. For a transmitting aerial (antenna) the optimal size is of the order of about half the wavelength, for maximum transmitting power. The fraction "dipole-size over wavelength" is more favourable for short wavelengths. Thus, more light with short waves is scattered than with long waves, inversely proportional to the fourth power of the wavelength. Light with 450 nm wavelength (blue) is scattered more than four times stronger than light of 650 nm (red).

This causes the sky to be blue."

Note: The experiment conducted is not a precise demonstration of Rayleigh Scattering, but a process similar caused by the Tyndall Effect.

The Tyndall Effect is similar to Rayleigh Scattering in that incident photons are randomly scattered in various directions and that the effect becomes more pronounced at higher frequencies. The primary difference between Rayleigh Scattering and the Tyndall Effect is that the particles involved with the Tyndall Effect are of much greater size than those associated with Rayleigh Scattering. The general concepts behind the Tyndall Effect are the same though the specific mathematical relations differ. Everyday examples of the Tyndall Effect are more common and include the way light is reflected off dust particles in a dark room as well as in the color and opacity of translucent gems.

Questions & Answers: Give three thought-provoking questions and provide detailed answers.

1) Question: Why isn't the sky violet? Since the degree of scattering is inversely proportional to the fourth power of the wavelength of light, violet light should scatter more....

Approximate wavelength of violet light: 400nm

Approximate wavelength of blue light: 480nm

(violet) (blue)

1 > 1

25600000000 53084160000

According to the math, violet light should scatter to a higher degree.

1) Answer: There are two reasons why the sky does not appear to be violet.

1. In the light spectrum of the sun, wavelength emission distribution is not equal.

2. The retina of your eye has two types of light-detecting cells: rods and cones. The sensitivity of rods and cones is dependent on the color

of the light. As the diagram shows, the eye perceives blue to a than violet. So, even though violet light is scattered to a higher

degree, human eyes do not detect it.

2) Question: So, why is the sky red during sunset?

2) Answer:

"At sunrise or sunset, sunlight takes a much longer path through the atmosphere than during the middle part of the day. Because an increased amount of violet and blue light is scattered out of the beam along the way, the light which reaches an observer early or late in the day is reddened."

(Image and explanation from: http://www.spc.noaa.gov/publications/corfidi/sunset/)

Applications to Everyday Life:

The effects of Rayleigh Scattering can be seen when the affected frequencies lie within the visible light spectrum.

Color of the sky - Since blue light is of higher frequency radiation than other colors of visible light, it is much more affected by Rayleigh Scattering. The most notable example of this is in the sky, where Rayleigh Scattering caused by gases in the atmosphere scatter blue light from the sun while allowing most other frequencies of light to pass unperturbed.

Fiber Optics - Optical fibers are typically constructed from glass or plastic materials. Manufacturing processes cannot make the fibers perfectly homogenous so ‘density fluctuations’ are present throughout the material. This results in Rayleigh scattering which diminishes the strength of the optical signal (i.e. light intensity) with increasing irregularities. Overall, this is the cause of 96% of signal loss in optical fibers.

Eye Color - Pigments found in human irises only range between brown and black. Other types of eye colors such as green, blue, and hazel result from light scattering of the Tyndall Effect. Higher frequency light will be scattered more than lower frequency light entering the iris and scattering thresholds will vary depending on eye color. This is the reason why some people’s eyes seem to change color in different lighting conditions.

(http://www.itp.uni-hannover.de/~zawischa/ITP/scattering.html)

The iris of the human eye does not contain any blue pigment or dye. The turbid front layer, if it contains no or only little melanin, appears blue in front of the dark back layer due to the preferred scattering of light with short wavelengths.

Photographs: Include a photograph of you or students performing the experiment/demonstration, and a close-up, easy to interpret photograph of the activity --these can be included later.

Videos: Include links to videos posted on the web that relate to your activity. These can be videos you have made or ones others have made.