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Blue sky

This is the outline for a future lesson on Rayleigh Scattering: Why the sky is blue

– Rayleigh scattering occurs when light is scattered off many very small particles.
– Mie scattering occurs when light is scattered off of many larger particles.


Addressing misconceptions

Question: Particles in the air cause shorter wavelengths (blue-ish0 to scatter more than the longer wavelengths (reddish.) This causes us to see the sky as being blue. So why does the sunrise (or sunset) and sun look red/orange?

Answer: “When you look at the sky and see blue you’re seeing blue light being scattered towards your eye.”

“When you look at the sun and it looks red or orange that’s because the blue light is being scattered away from your eye – leaving the remaining light to enter your eye.”

“The blue light is being scattered in all directions by Raleigh scattering. The colors you see depend on what direction you’re looking.”

Reference Physicsforums.com How-does-rayleigh-scattering-work


External resources





Brownian motion app  galileoandeinstein Brownian motion app

Lesson EarthRef.org Digital Archive ematm.lesson3.scattering.pptx

EM in the Atmosphere: Reflection, Absorption, and Scattering Lesson Plan

Powerpoint for the lesson plan

Learning standards

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color

AP Learning Objectives

IV.A.2.b: Students should understand the inverse-square law, so they can calculate the intensity of waves at a given distance from a source of specified power and compare the intensities at different distances from the source.

IV.B.2.b: Know the names associated with electromagnetic radiation and be able to arrange in order of increasing wavelength the following: visible light of various colors, ultraviolet light, infrared light, radio waves, x-rays, and gamma rays.

L.2: Observe and measure real phenomena: Students should be able to make relevant observations, and be able to take measurements with a variety of instruments (cannot be assessed via paper-and-pencil examinations).

L.3: Analyze data: Students should understand how to analyze data, so they can:
– a) Display data in graphical or tabular form.
– b) Fit lines and curves to data points in graphs.

L.5: Communicate results: Students should understand how to summarize and communicate results, so they can:
– a) Draw inferences and conclusions from experimental data.
– b) Suggest ways to improve experiment.
– c) Propose questions for further study

Study guide

Work  Review these webnotes, and the linked review sheets at the bottom of the page.
Pay close attention to the diagrams.  Review “Skill Sheet 5A-Work”

Energy  Review these webnotes. The linked Animations on work and energy are useful. So is the roller coaster physics section. Review the handouts on energy

Power  Skill Sheet 5A-Power. Follow the examples!

Heat and Thermal Energy  Use the 2 pages of review questions that you received for the chapter review.

Heat: Changes of State  Consider fig. 12 Temperature vs Heat, p.330.  Click on “Details on Changes of State” for more notes

Sample problem: Release a roller coaster car from point A. how fast is going at point D?

How would you use conservation of energy to solve a problem like this?

Big idea: All energy at A is PE.  At point D, all of that energy is converted to PE

Set KE = PE.   Use the correct terms from the equation.

Then solve for the velocity.  In the final step, plug in the numbers.



The Sumerian hero Gilgamesh traveled the world in search of a way to cheat death. On one of his journeys, he came across an old man, Utnapishtim, who told Gilgamesh a story from centuries past. The gods brought a flood that swallowed the earth.

Gilgamesh Rainbow Magic Dawkins

The Magic of Reality: How We Know What’s Really True [Richard Dawkins]

The gods were angry at mankind so they sent a flood to destroy mankind. The god Ea, warned Utnapishtim and instructed him to build an enormous boat to save himself, his family, and “the seed of all living things.” He does so, and the gods brought rain which caused the water to rise for many days.

When the rains subsided, the boat landed on a mountain, and Utnapishtim set loose first a dove, then a swallow, and finally a raven, which found land. The god Ishtar, created the rainbow and placed it in the sky, as a reminder to the gods and a pledge to mankind that there would be no more floods.  A similar story, with theological modifications, is in the Hebrew Bible as the story of Noah and the Ark.

This story comes from the Epic of Gilgamesh

In physics we learn that rainbows are produced by electromagnetic radiation – visible light – reflecting in marvelous ways from the dispersion of light.

Let’s start with the basics:

A prism separates white light into many colors

How? Each wavelength of light refracts by a different amount

The result is dispersion – each wavelength is bent by a different amount


Rebecca McDowell put together this lesson on rainbow formation. She created the graphics using CorelDRAW and CorelPHOTOPAINT. From How rainbows form

Introduction: The formation of a rainbow involves a series of physical phenomena:

reflection, refraction, dispersion and total internal reflection.


http://www.rebeccapaton.net/rainbows/formatn.htm Copyright 1999 Rebecca McDowell.

Let’s break this down



1. Light from sun strikes raindrop.

White light from the Sun has to hit the raindrops at a certain angle before a rainbow is possible. It is best if the sun is fairly low in the sky such as dawn and late afternoon. The angle is important as it effect the direct the light travels after it hits the raindrops and that determines whether or not we will see a rainbow.

2. Some of the light is reflected.

It is possible to see through a glass window but, at the same time, see your own reflection. This is because the window both transmits and reflects light. Water can do this too – that is why you can see a reflection in a pool of clean water and also see the bottom.

When light from the sun hits a water droplet, some of the light is reflected. This light will obey the Law of Reflection.

3. The rest of the light is refracted.

The light that is not refracted crosses the air-water interface (boundary layer). When this happens it slows down because the water is more dense than the air. The reduction of speed cause the path of the light to bend – this is called refraction. In this case the path of the light rays bends toward the normal line.

4. White light splits into component colours.

White light is made up of a spectrum of colours, each with its own wavelength. Different wavelengths travel at different speeds and when they encounter a change to medium that is more dense or less dense, the speeds are efected by different amounts. Hence, the colours separate. This phenomenon is know as Dispersion.

5. Light is reflected at rear of raindrop (TIR).

At the rear of the raindrop, the light hits the water-to-air interface. If the angle of incidence is greater than the critical angle, Total Internal Reflection will occur. A rainbow will only be seen if this happens, otherwise the light will continue out the other side of the raindrop and continue to move away from the would-be viewer.

6. Light is refracted again as it leaves raindrop.

Just as the light changed speed as it entered the raindrop, its speed changes again as it leaves. Here, the light is moving from a more dense medium (water) to a less dense medium (air). As it does so, it speeds up and its path bends. In this case the path of the light rays bends away from the normal line. This is another example of refraction.

7. Colours are further dispersed.

As the rays are refracted once again, the various wavelengths are effected to different extents. The overall result of this is increased separation of the component colours of white light. This is Dispersion.

Do rainbows have reflections?

It certainly seems like rainbows can have reflections. Consider this great photo by Terje O. Nordvik, September ’04 near Sandessjøen, Norway.

But rainbows aren’t real objects – and so they literally can’t have reflections!
So what are we seeing here? See Rainbow reflections: Rainbows are not Vampires


Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-3. Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described by either a wave model or a particle model, and that for some situations involving resonance, interference, diffraction, refraction, or the photoelectric effect, one model is more useful than the other.

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color.


MCAS light and optics practice problems

MCAS example problems

Which of the following statements describes what will most likely happen to the light ray after it strikes the aluminum foil?

A. The light ray will be absorbed by the shiny metal.
B. The light ray will be refracted after passing through the shiny metal.
C. The light ray will be reflected at a different angle to the normal than the incident light ray.
D. The light ray will be reflected at the same angle to the normal as the incident light ray





2016 Physics MCAS



Physics MCAS 2014



Physics MCAS 2014


a. Identify and describe the wave behavior as the light rays pass through the glass lens.

b. Identify and describe the wave behavior as the light rays strike the mirror.

c. Copy the dotted box from the camera diagram into your Student Answer Booklet. Draw what must happen inside the box for light ray 2 to strike the viewfinder. Be sure to include
the following:
• either a lens or a mirror that is labeled
• the path of light ray 2
• a line normal to the surface where light ray 2 strikes

Schrödinger’s cat

Text adapted from “Schrödinger’s cat.” Wikipedia, The Free Encyclopedia, 5 Feb. 2017.


Schrödinger’s cat is a thought experiment, sometimes described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects.

Cat static balloons

Schrödinger’s cat: a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal monitor detects radioactivity (i.e., a single atom decaying), the flask is shattered, releasing the poison, which kills the cat. The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead.


This poses the question of when exactly quantum superposition ends and reality collapses into one possibility or the other.

The Copenhagen interpretation implies that the cat remains both alive and dead – until the state is observed.

Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility.

On the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics


Since Schrödinger’s time, other interpretations of quantum mechanics have been proposed that give different answers to the questions posed by Schrödinger’s cat of how long superpositions last and when (or whether) they collapse.

Many-worlds interpretation and consistent histories

In 1957, Hugh Everett formulated the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process.

In the many-worlds interpretation, both alive and dead states of the cat persist after the box is opened, but are decoherent from each other.


In other words, when the box is opened, the observer and the possibly-dead cat split into an observer looking at a box with a dead cat, and an observer looking at a box with a live cat. But since the dead and alive states are decoherent, there is no effective communication or interaction between them. We have created parallel universes!

Decoherence interpretation

When opening the box, the observer becomes entangled with the cat, so “observer states” corresponding to the cat’s being alive and dead are formed; each observer state is entangled or linked with the cat so that the “observation of the cat’s state” and the “cat’s state” correspond with each other. Quantum decoherence ensures that the different outcomes have no interaction with each other. The same mechanism of quantum decoherence is also important for the interpretation in terms of consistent histories. Only the “dead cat” or the “alive cat” can be a part of a consistent history in this interpretation.


External resources





A cheetah’s tail provides an excellent example of torque and angular momentum in action. With a simple clockwise flick of the tail, the cheetah’s body (in a response which conserves angular momentum) rolls in the anti-clockwise direction (and conversely).
This enables the cheetah to position its body mid-flight so that it is ready to turn the instant its feet make contact with the ground.




Triple point

The following is from the Learner.Org Chemistry course https://www.learner.org/courses/chemistry/about/about.html

Once the gas laws were formulated, chemists could analyze how materials transitioned from one phase to another, and how temperature and pressure affected these changes.

In 1897, a British metallurgist named Sir William Chandler Roberts-Austen (1843–1902) produced what is widely regarded as an early form of a now-common tool in chemistry and related disciplines: the phase diagram.

Modern phase diagrams show relationships between different states of matter under various combinations of temperature and pressure.

A substance can exist in two different states at once—for example, as a liquid and a gas, with molecules cycling from one state to the other.

It is also possible for a material to be both solid and liquid, with both melting and freezing taking place at its edges, or to exist as a solid and a gas.

Phase diagrams show what forms a substance will take under given temperatures and pressure levels, and where these equilibrium lines (when equal numbers of molecules are changing form in both directions) are located. (Figure 2-11)

Figure 2-11. Generic Phase Diagram for a Single Substance © Science Media Group. https://www.learner.org/courses/chemistry/text/text.html?dis=U&num=Ym5WdElUQS9NeW89&sec=YzJWaklUQS9OeW89

Figure 2-11. Generic Phase Diagram for a Single Substance
© Science Media Group.

Amazing: See a flask of liquid cyclohexane brought to the brink of its triple-point:
suddenly it can boil and freeze at the same time.


A volumetric flask containing liquid cyclohexane is depressurized to a very low pressure by a turbo-molecular vacuum pump. The rapid drop in pressure results in a rapid drop in temperature, causing the substance to temporarily freeze, but the system is unstable, flirting with the triple point (a point of pressure and temperature at which a substance is simultaneously solid, liquid, and gas). The result is a fluctuation between all three states of matter, in a spectacular display of chemistry and physics in action.