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MCAS Heat problems
Problems on heat and thermodynamics: Massachusetts Physics MCAS
2015 MCAS Physics Exam
#4. The graph below shows how the temperature of a sample of water changes as energy is added to the sample.

During which interval does a gas form?
A. Q to R
B. R to S
C. S to T
D. T to U
_ _ _ _ _ _ _ _ _ _ _ _ _ _
#21. Sunlight warms an area of Earth’s surface. Winds then carry thermal energy from this area to another location. Which two heat transfer processes are primarily involved in this situation?
A. radiation and convection
B. radiation and evaporation
C. conduction and convection
D. conduction and evaporation
_ _ _ _ _ _ _ _ _ _ _ _ _ _
#24. Frozen food is submerged in a small insulated container of 95°C water. Which statement best describes the temperature of the food after two hours, assuming no heat is lost outside of the insulated container?
A. The temperature of the food will be 95°C.
B. The temperature of the food will be 100°C.
C. The temperature of the food will be the same as the temperature of the water.
D. The temperature of the food will be greater than the temperature of the water.
_ _ _ _ _ _ _ _ _ _ _ _ _ _
#31 A student heats 200 g of water from 20°C to 70°C. How much heat did the student add to the water if the specific heat for water is 4.2 J/g C •° ?
A. 10,000 J B. 14,000 J
C. 42,000 J D. 76,000 J
_ _ _ _ _ _ _ _ _ _ _ _ _ _
#44 A student was investigating cooling times for two pots made of different materials. One pot was stainless steel and the other pot was iron. The pots were placed on a table in a 25°C room. The pots were roughly the same size and shape, and contained the same amount of water. The pots and water were originally at 100°C. The student recorded the temperature of the water in each pot over time. The graph below shows the results.

a. Determine the amount of time it took the water in the iron pot to cool from 100°C to 60°C.
b. Based on the graph, which pot, the iron pot or the stainless steel pot, was a better conductor of thermal energy? Explain your answer.
c. Identify two methods of heat transfer that occurred as the water in the pots cooled, and describe how the transfer of heat occurred for each method.
d. Describe when the pots no longer experienced a net loss of thermal energy.
2016 MCAS Physics Exam
A 1 kg sample of liquid water and a 1 kg sample of ice are placed on a table. Which of the following statements best compares these two samples?
A. The liquid water has a larger volume than the ice.
B. The liquid water has a greater weight than the ice.
C. The liquid water has more thermal energy than the ice.
D. The liquid water has more gravitational potential energy than the ice.
_ _ _ _ _ _ _ _ _ _ _ _ _ _
6. Two U.S. quarters, initially at the same temperature, are heated with a flame. One of the quarters was made before 1965 and is composed of silver. The
other quarter was made after 1965 and is composed mostly of copper.
What information is needed to determine which quarter will heat up faster?
A. the specific heats of the metals and the mass of each coin
B. the initial temperature of the coins and the mass of each coin
C. the temperature of the flame and the specific heats of the metals
D. the initial temperature of the coins and the temperature of the flame
_ _ _ _ _ _ _ _ _ _ _ _ _ _
16. A fan enables a computer’s processor to run for long periods of time without overheating. Which of the following forms of heat energy transfer does this
example best represent?
A. condensation
B. convection
C. evaporation
D. radiation
_ _ _ _ _ _ _ _ _ _ _ _ _ _
18. A small steel rod is placed in 5 L of water. The initial temperature of the steel rod is 120°C, and the initial temperature of the water is 10°C. When does heat stop flowing between the steel rod and the water?
A. when the steel rod reaches 65°C
B. when the water reaches its boiling point
C. when the steel rod reaches 10°C and the water reaches 120°C
D. when the steel rod and the water reach the same temperature
_ _ _ _ _ _ _ _ _ _ _ _ _ _
27. Two identical objects, one hot and one cold, are placed near each other in a closed system. Which of the following graphs shows what happens to the temperatures of the objects over time?
_ _ _ _ _ _ _ _ _ _ _ _ _ _
44. During cold periods, many orange growers repeatedly spray their trees with water to prevent the oranges from freezing. If the air is cold enough, the sprayed water freezes around the oranges, leaving the oranges themselves unfrozen.
a. Identify a measurement tool that orange growers use to measure the average kinetic energy of the air.
b. Describe what happens to the average molecular kinetic energy of the sprayed water
as it cools before it freezes.
c. Describe what happens to the average molecular kinetic energy of the sprayed water
as it freezes.
d. Explain how the phase change of the sprayed water may protect the oranges from freezing.
_ _ _ _ _ _ _ _ _ _ _ _ _ _
Sample “Open Response” answers: Question 44: Open-Response
Question 44: Open-Response
Reporting Category: Heat and Heat Transfer
Standard: 3.1 – Explain how heat energy is transferred by convection, conduction, and radiation.
A student was investigating cooling times for two pots made of different materials. One pot was stainless steel and the other pot was iron. The pots were placed on a table in a 25°C room. The pots were roughly the same size and shape, and contained the same amount of water. The pots and water were originally at 100°C. The student recorded the temperature of the water in each pot over time. The graph below shows the results.

a. Determine the amount of time it took the water in the iron pot to cool from 100°C to 60°C.
b. Based on the graph, which pot, the iron pot or the stainless steel pot, was a better conductor of thermal energy? Explain your answer.
c. Identify two methods of heat transfer that occurred as the water in the pots cooled, and describe how the transfer of heat occurred for each method.
d. Describe when the pots no longer experienced a net loss of thermal energy.
Scoring Guide and Sample Student Work
| Score | Description |
|---|---|
| 4 | The response demonstrates a thorough understanding of heat transfer by convection, conduction, and radiation and of thermal equilibrium. The response correctly determines the time it took for water in the iron pot to cool to 60°C, and clearly explains which pot is a better conductor. The response also correctly identifies and clearly describes two methods of heat transfer that occurred as the water cooled, and describes when the pots no longer experienced a net loss of thermal energy. |
| 4 | |
| 3 | The response demonstrates a general understanding of heat transfer by convection, conduction, and radiation and of thermal equilibrium. |
| 2 | The response demonstrates a limited understanding of heat transfer by convection, conduction, and radiation and of thermal equilibrium. |
| 1 | The response demonstrates a minimal understanding of heat transfer by convection, conduction, and radiation and of thermal equilibrium. |
| 0 | The response is incorrect or contains some correct work that is irrelevant to the skill or concept being measured. |
Note: There are 2 sample student responses for Score Point 4.
MCAS wave problems
MCAS Physics exam: Example Problems

MCAS 2011
Which of the following describes and explains what the observer hears as the buzzer moves away from him?
A. a lower-pitched buzz than the buzzer’s normal sound because the sound waves are arriving less frequently
B. a higher-pitched buzz than the buzzer’s normal sound because the sound waves are arriving more frequently
C. a lower-pitched buzz than the buzzer’s normal sound because the velocity of the sound waves is reduced by the velocity of the swinging buzzer
D. a higher-pitched buzz than the buzzer’s normal sound because the velocity of the sound waves is increased by the velocity of the swinging buzzer
#25, MCAS 2011

#32. Essay question, MCAS 2011
A large anchor is being lifted into a boat with metal sides. As the anchor leaves the water it
hits the side of the boat, making loud sounds and making waves on the surface of the water.
a. Describe the motions of the sound waves and the water waves.
b. Draw a diagram for each of the waves you described in part (a). Be sure to label each
diagram.
c. Describe how the wavelength is measured for the water waves
#35. Which of the following observations demonstrates that visible light waves are
electromagnetic and not mechanical?
A. Sunlight can pass through gas.
B. Sunlight can pass through solids.
C. Sunlight can pass through liquids.
D. Sunlight can pass through a vacuum.
#37, MCAS 2011
Which of the following statements best explains why lightning is seen before thunder is heard?
A. Electromagnetic waves travel faster than mechanical waves in air.
B. Electromagnetic waves have a higher frequency than mechanical waves.
C. Electromagnetic waves experience less interference than mechanical waves.
D. Electromagnetic waves form faster than mechanical waves during a thunderstorm.
#3, MCAS 2011
In a large room, a sound wave traveling from a violin produces a tone with a frequency of 264 Hz. The speed of sound in the room is 340 m/s. What is the wavelength of the sound wave from the violin?
A. 0.004 m B. 0.80 m C. 1.3 m D. 2.6 m
MCAS 2012
2. When music plays through the speaker, the speaker rapidly moves back and forth in the cabinet. Which of the following conclusions is best supported by this observation?
A. Sound travels only in air.
B. Sound is a transverse wave.
C. Sound is a longitudinal wave.
D. Sound travels at the speed of light
4. Which of the following statements best describes a difference between mechanical waves and electromagnetic waves?
A. Mechanical waves can produce colored light, while electromagnetic waves cannot.
B. Mechanical waves can travel in any direction, while electromagnetic waves travel only in one direction.
C. Mechanical waves travel only through a medium, while EM waves can also travel through a vacuum.
D. Mechanical waves travel only at the speed of light, while electromagnetic waves can travel at many different speeds.
6. A student is sitting on the edge of a swimming pool. The student repeatedly dips his foot in and out of the pool, making waves that move across the water. The student dips his foot slowly at first and then does it faster, each time to the same depth. Which of the following properties of the waves increases as the student dips his foot faster?
A. frequency
B. period
C. velocity
D. wavelength
21. A rope is stretched horizontally between two students. One of the students shakes an end of the rope up and down. Which of the following terms best describes the type of wave that is produced?
A. electromagnetic
B. longitudinal
C. rotational
D. transverse
#26. MCAS 2012

#29. Student X and student Y are receiving sound waves from a stationary source. The sound waves have a frequency of 10 kHz. Student X is stationary and student Y is traveling toward the source of the sound waves.
Which of the following statements describes what will happen as student Y moves?
A. Student X will receive sound waves with a frequency higher than 10 kHz.B. Student X will receive sound waves with a frequency lower than 10 kHz.
C. Student Y will receive sound waves with a frequency higher than 10 kHz.
D. Student Y will receive sound waves with a frequency lower than 10 kHz.
#37 Two waves traveling in the same medium are shown below.

Which of the following correctly compares the two waves?
A. Wave X has half the amplitude of wave Y.
B. Wave X has twice the amplitude of wave Y.
C. Wave X has a lower frequency and longer wavelength than wave Y.
D. Wave X has a higher frequency and shorter wavelength than wave Y
#42 In which of the following media do sound waves most likely travel the fastest?
A. crude oil
B. distilled water
C. solid steel
D. warm air
MCAS 2013
#2. A student is shaking one end of a small rug with a ball on top of it. The wave that is produced travels through the rug and moves the ball upward, as shown in the diagram below

#6. A person is driving north in a car at a constant speed. A police officer is
driving south toward him at a constant speed. The police officer uses a radar
unit to measure the speed of the person’s car. The radar unit sends out waves of
a certain frequency toward the person’s car. The waves reflect off the person’s car and travel back to the radar unit in the police car. What happens to the frequency of the waves detected by the radar unit?
A. The frequency is lower as the person’s car approaches.
B. The frequency is higher as the person’s car approaches.
C. The frequency remains the same but with increased energy as the person’s car approaches.
D. The frequency remains the same but with decreased energy as the person’s car approaches.
#22. Which of the following properties makes a light wave different from all mechanical waves?
A. A light wave slows down in a vacuum.
B. A light wave is able to transmit energy.
C. A light wave exists as a transverse wave.
D. A light wave can travel without a medium
#25. Which of the following observed properties of a wave is changed by the Doppler effect?
A. amplitude
B. direction
C. frequency
D. speed
#28. The diagram below shows two students making a wave with a coiled spring

MCAS 2014
#2. Waves rock a boat in the middle of a pond. The boat moves up and down 10 times in 20 seconds. What is the period of the waves?
A. 0.5 s B. 2 s C. 10 s D. 20 s
#16. A sound wave with a frequency of 1,700 Hz is traveling through air at a speed of 340 m/s. What is the wavelength of this sound wave?
A. 0.2 m B. 5.0 m C. 2,040 m D. 57,800 m
#19. Sunscreen protects skin by absorbing harmful ultraviolet radiation from the Sun. Ultraviolet radiation has which of the following properties?
A. a shorter wavelength than x-rays
B. a lower frequency than radio waves
C. a higher frequency than visible light
D. a longer wavelength than microwaves
#23. ESSAY. Waves can be classified as either electromagnetic or mechanical.
a. Describe two differences between electromagnetic and mechanical waves.
b. Give two examples of electromagnetic waves.
c. Give two examples of mechanical waves.
#26. A wave with a wavelength of 3.2 m is generated in a pond. The frequency of the wave is 0.60 Hz. What is the speed of this wave?
A. 0.19 m/s
B. 1.9 m/s
C. 3.8 m/s
D. 5.3 m/s
#30. The diagram below shows a representation of two different waves

MCAS 2015
14. A train driver blows the train’s horn as it moves away from a station. Which of the following statements describes how the sound of the horn heard by an observer standing at the station platform differs from the sound heard by the train driver?
A. The observer hears the sound as having a greater velocity.
B. The observer hears the sound as having a lower frequency.
C. The observer hears the sound as having a greater amplitude.
D. The observer hears the sound as having a shorter wavelength
#17. A windsurfer moves at 5 m/s while staying on the crest of a wave, as shown below.

#29. A seismic wave called a P-wave travels through the solid part of Earth. In a P-wave, the solid particles of Earth move parallel to the direction the P-wave travels. P-waves are which of the following types of waves?
A. electromagnetic
B. longitudinal
C. torsional
D. transverse
#38. At a given temperature, a longitudinal mechanical wave will travel fastest through which of the following?
A. a gas
B. a liquid
C. a solid
D. a vacuum
#45. Essay and Drawing! A floating object moves up and down 15 times in 60 s because of ocean waves.
a. Calculate the period of the ocean waves. Show your calculations and include units in
your answer.
b. Calculate the frequency of the ocean waves. Show your calculations and include units in
your answer.
An additional wave property must be known in order to calculate the velocity of the ocean
waves.
c. In your Student Answer Booklet, identify this additional wave property and draw a wave
diagram showing how the property can be measured.
d. Describe what will happen to the object if the amplitude of the ocean waves increases and all other wave characteristics stay the same
**
Textbook p.393, #18.
How does increasing the wavelength of a rope by 50 % decreases its frequency by 33 %.
The relation between frequency and wavelength is
fλ=v
Then
f1λ1 = f2λ2
If f1 = f, then f2 = 1.50f
λ2 = λ1 × f1f2 = λ1 × f1.50f = 0.67λ1
The new wavelength is 67 % of the original (33 % less than the original).
Learning Standards
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium
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
Peer review
This resource contains 2 lessons

Enter a caption
Image courtesy of the UC San Diego Library
(1) Scrutinizing science: Peer review. UC Museum of Paleontology of the University of California at Berkeley.
(2) In search of quality: The scientific peer review process. EUFIC – The European Food Information Council. A non-profit organisation for science-based information on food and health.
______________________________________________
Scrutinizing Science: Peer Review
Peer review does the same thing for science that the “inspected by #7” sticker does for your t-shirt: provides assurance that someone who knows what they’re doing has double-checked it. In science, peer review typically works something like this:
-
A group of scientists completes a study and writes it up in the form of an article. They submit it to a journal for publication.
-
The journal’s editors send the article to several other scientists who work in the same field (i.e., the “peers” of peer review).
-
Those reviewers provide feedback on the article and tell the editor whether or not they think the study is of high enough quality to be published.
-
The authors may then revise their article and resubmit it for consideration.
-
Only articles that meet good scientific standards (e.g., acknowledge and build upon other work in the field, rely on logical reasoning and well-designed studies, back up claims with evidence, etc.) are accepted for publication.

Peer review and publication are time-consuming, frequently involving more than a year between submission and publication. The process is also highly competitive. For example, the highly-regarded journal Science accepts less than 8% of the articles it receives, and The New England Journal of Medicine publishes just 6% of its submissions.
Peer-reviewed articles provide a trusted form of scientific communication. Even if you are unfamiliar with the topic or the scientists who authored a particular study, you can trust peer-reviewed work to meet certain standards of scientific quality.
Since scientific knowledge is cumulative and builds on itself, this trust is particularly important. No scientist would want to base their own work on someone else’s unreliable study!
Peer-reviewed work isn’t necessarily correct or conclusive, but it does meet the standards of science. And that means that once a piece of scientific research passes through peer review and is published, science must deal with it somehow — perhaps by incorporating it into the established body of scientific knowledge, building on it further, figuring out why it is wrong, or trying to replicate its results.
– Scrutinizing science: Peer review. UC Museum of Paleontology of the University of California at Berkeley.
______________
In search of quality: The scientific peer review process
Before a scientific assertion is made public it should be scrutinised for its credibility. Has the scientist drawn justifiable conclusions, based on the data available from sound scientific research?
The peer review process is a form of scientific quality control, where scientists open their research to the scrutiny of other experts in the field (peers).1
By reviewing and criticising each others’ work, scientists aim to ensure that only original and sound research is published and recognised.
How does it work?
When research is submitted for publication in a peer-reviewed journal, the journal invites several (usually two or more) independent experts to assess the credibility of the research.1
These experts consider the scientific methods, results and conclusions presented by the authors, asking themselves, if the science is technically sound, if the interpretation is consistent with the data, and if it is new, important or ground-breaking.2
Reviewers usually remain anonymous, are not paid for their assessment, and should not have any conflicts of interest in relation to the research. If a paper does not meet the requirements, based on the peer reviews, the editor can either reject it or deem it acceptable subject to adequate changes, allowing authors to react and revise their paper.
Why is it important?
The peer review process checks that a paper explains clearly how the research was carried out, so that it can be reproduced by others. It also verifies that the methodology is appropriate for the specific field and set of objectives.
Another crucial part of the review process is assessing the originality of new research and the accurate referencing of related published research, particularly if these contrast with the research at hand. The review is also useful for those whose work is being scrutinised; it allows them to fine-tune their manuscript before public release.2
A manuscript is seldom accepted for publication without at least a minor revision.
The review process essentially strives to separate fact from speculation and personal opinion.2
Peer-reviewed research is never beyond criticism however, and any conclusions drawn must be considered in the context of other studies. Ideally, experiments should be repeated to assess whether results can be reproduced; this is how findings are truly substantiated. The real validation, therefore, comes after publication.
Non-peer-reviewed research
Unfortunately, research results often find their way into the public domain without being peer reviewed, and are spread via newspapers, magazines, the internet, television and radio. They may be unpublished findings presented at press conferences, or published findings from a journal that does not use peer review.
Even journals that do use peer review contain some non-peer-reviewed content, such as editorials and letters to the editor. Both scientists and journalists should understand the meaning and importance of peer review and clarify whether or not research they discuss has been peer-reviewed. There are potentially enormous costs to both science and society from the promotion of scientifically weak or flawed research findings.
An imperfect process
The peer review process does not protect against misconduct. It can identify mistakes, but relies on honesty and, as a result, can fail to recognise deliberately fraudulent research. Various organisations have produced integrity guidelines on good research practice aiming to reduce such occurrences.3
On the other side, financial or personal concerns may bias a reviewer’s professional judgement and objectivity. It is vital to consider in advance any factors, which could lead to bias.3
According to the European Science Foundation, preventing and managing such conflicts of interest is crucial in ensuring equity and integrity.3
Sometimes concerns are raised about the influence of the funding body on the design of the study, or the interpretation or reporting of the research outcomes. The peer review process gives credence to research, because the paper has been independently checked and critically evaluated, including the correct scientific interpretation of the results on the basis of other existing evidence – no matter who funded the research.2
Inevitably, there are variations in standards between journals. A journal’s “Impact Factor” reflects how often its papers are cited in other peer-reviewed journals, and gives some indication of importance of the journal in its field – the higher the number, the greater the impact or influence.
The process and culture of checking each other’s work is ongoing in the scientific world. Once a paper has been published, further criticism can be made by the scientific community via letters to the journal editor, discussions at conferences, or direct exchange with the research team behind the study in question. Authors can justify their findings and flaws uncovered can be corrected or retracted.1,2
This is the nature of science; all work is open to critique by other scientists.
References
- Science Media Centre (2012). Peer review in a nutshell: http://www.sciencemediacentre.org/wp-content/uploads/2012/09/Peer-Review-in-a-Nutshell.pdf
- Sense About Science (2004). Peer Review and the acceptance of new scientific ideas. London: Sense About Science. http://www.senseaboutscience.org/data/files/resources/17/peerReview.pdf
- European Science Foundation (2011). European peer review guide integrating policies and practices into coherent procedures. Strasbourg: European Science Foundation. http://www.vr.se/download/18.2ab49299132224ae10680001647/European+Peer+Review+Guide.pdf
Related ideas
Welcome to the Journal of Alternative Facts 🙂
Waves in 2 dimensions
Let’s throw a stone into water and then observe the circular crests and troughs
We see waves propagate in 2 dimensions: along the X-axis, and Y-axis, simultaneously.
Awavefront represents the crest of a wave in 2 dimensions
2-dimensional waves always travel perpendicular to their wavefronts
A wave’s direction is represented by a ray
Here, water waves, or light waves, hit a curved surface
The wavefronts reflect to a point, called the focus.
Refraction of 2-D waves
Refraction is the change in direction of wave propagation due to a change in its transmission medium.
Often seen with light.
Seen with water waves, when they move from deep water into shallow water.
Here light waves refrac as they move from one medium into another (from air into diamond)
In this simplified case, the light waves (or water waves) are all parallel to each other.
Here we see the same thing, but now the rays of light are more realistic.
They emanate from a source, so they are circular, not parallel.
Yet when the rays hit the water, they are approximately parallel, so the result is the same.

Snell’s law at PhysicsClassroom.com
Water waves can be refracted
Animation GCSE Light and water refraction
Here we see water waves changing direction, as they enter shallower waters.

From a presentation by Luo Yanjie.
From a presentation by Luo Yanjie.
Details on the cause of refraction (PhysicsClassroom.Com)
Learning Standards
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium
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
How a computer interprets instructions
How does a computer understand (interpret and execute) a high level programming language?

What’s the difference between a high-level computer language and a low-level language? How does a computer interpret these languages, so the program can run? What is computer programming?
How does a computer understand a computer program http://guyhaas.com/bfoit/itp/Programming.html
BBC Bitesize Revision: Running a program, the CPU, etc. (a 5 page step-by-step resource) http://www.bbc.co.uk/education/guides/z2342hv/revision/1
How do you communicate with computers? Through a programming language. Source code and language differences: Learntocodewith.me
Break down how code gets translated from the code programmers write, to the code computers read, the difference between compiled and interpreted code, and what makes “just-in-time” compilers so fast and efficient. The Basics of Compiled Languages, Interpreted Languages, and Just-in-Time Compilers
How do computers understand programming languages? How do you “teach” a computer a language? Explanation by Christian Benesch, software engineer and architect (among other explanations) here
How does a computer understand a computer program? Codeconquest.com How does coding work?
What is a program? What is a programming language? Depending on the language used, and the particular implementation of the language used, the process to translate high-level language statements to actions may involve compilation and interpretation. Introduction to Programming (Wikiversity)
Subtractive color
There are 2 ways to create color:
additive model/RGB:
Make new colors by adding beams of light
RGB: red, green, blue
subtractive model/CMYK:
Making new colors by adding pigments (dyes, inks, paints)
CMYK: Cyan, Magenta, Yellow, Black
This lesson is on the subtractive color model.

Paints/inks/dyes contain pigments, molecules that absorb some frequencies of light, but not others.
When paints/inks/dyes are mixed, the mixture absorbs all the frequencies that each individual one absorbs.
Examples:
Blue paint absorbs red, orange, and yellow light. It reflects the rest (blue, violet, some green)
Yellow paint absorbs blue & violent. It reflects mostly yellow, and some red, orange, and green.
Images by Paul Hewitt

Mixing colored light is called color mixing by addition.
When you cast lights on a stage, you use the rules of color addition, but when you mix paint, you use the rules of color subtraction.
The three colors most useful in color mixing by subtraction are:
• magenta (bluish red)
• yellow
• cyan (greenish blue)
Magenta, yellow, and cyan are the subtractive primary colors, used in printing illustrations in full color.

Color printing is done on a press that prints each page with four differently colored inks (magenta, yellow, cyan, and black).
• Each color of ink comes from a different plate, which transfers the ink to the paper.
• The ink deposits are regulated on different parts of the plate by tiny dots.
• The overlapping dots of three colors plus black give the appearance of many colors.

SlideShare on Color and Light
Learning Standards
SAT subject test in Physics: Waves and optics
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color.
Massachusetts Arts Curriculum Framework: The Practice Of Creating
PreK- 4 Visual Arts Standards – Identify primary and secondary colors; predict and demonstrate the effects of blending or overlapping primary colors; demonstrate knowledge of making dark to light values of colors. Identify and use basic two-dimensional hollow and solid geometric shapes (circle, triangle, square, rectangle) and three-dimensional forms (sphere, pyramid, cube).
Grades 5-8 Visual Arts Standards – Create compositions that reflect knowledge of the elements and principles of art, i.e., line, color, form, texture; balance, repetition, rhythm, scale, and proportion. Demonstrate the ability to apply elements and principles of art to graphic, textile, product, and architectural design.
Massachusetts Arts Curriculum Framework
The Arts Disciplines: Visual Arts
PreK–12 STANDARD 2: Elements and Principles of Design
By the end of Grade 4: 2.1 Students will, for color, explore and experiment with the use of color in dry and wet media Identify primary and secondary colors and gradations of black, white and gray in the environment and artwork.
By the end of Grade 8: 2.7 Students will, for color, use and be able to identify hues, values, intermediate shades, tints, tones, complementary, analogous, and monochromatic colors. Demonstrate awareness of color by painting objective studies from life and freeform
abstractions that employ relative properties of color.
Additive color
There are 2 ways to create color:
additive model/RGB:
Make new colors by adding beams of light
RGB: red, green, blue
subtractive model/CMYK:
Making new colors by adding pigments (dyes, inks, paints)
CMYK: Cyan, Magenta, Yellow, Black
This lesson is on the additive color model.

This lesson is from Apple Valley High School
http://www.district196.org/avhs/dept/science/physics/physicsweb04/AVHSPhysics/color-notes.html
Additive color: mixing beams of colored light
We start with no light, and add colors of light together to get the final result.
Complementary colors: These are two colors (one primary, one secondary) which, when added together, make white light. They are:
magenta and green
yellow and blue
cyan and red
Three projectors emit the 3 primary colors of light (red, green, blue) on a “white” screen.
Where two of the primary colors overlap you’ll find a secondary color.
Where all three overlap you’ll find white light.
Complementary colors are always across the white spot from each other in this “color wheel”.

Mixing colors of light
We have a white screen. It can reflect any color of light we shine on it.
Now shine red light on the surface – and hold up a hand so we cast a shadow.
The shadow will have no light hitting it so it will be black, while the rest of the screen would reflect the red light.

Now let’s add a green light on the right side of the picture.
Check out what happens now!

Notice how the screen has both green and red which makes yellow.
The shadow on the left blocks the green light, so the red light is the only light that hits that particular shadow.
The right shadow is green for the same reason. Cool, huh?
Now let’s add blue in the center. Check it out!

The screen has gone to white since it has red, green and blue striking it’s surface.
It reflects all 3 colors back to our eyes, so we see white.
The shadows are now the secondary colors (magenta, yellow, cyan).
This is because each shadow has 2 of the 3 primary colors hitting it, so it becomes one of the secondary colors.
Note: All of this is ONLY for mixing rays of light.
If you try mixing pigments (the colored chemicals in paints, crayons, dyes, markers, etc) we will get totally different results.
Looking at a white object in a white light

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Problems
When three colored lamps, red, blue and green, illuminate a physics instructor in front of a white screen in a dark room, three slightly overlapping shadows appear. Specify the colors in regions 1 through 6.

http://dev.physicslab.org/Document.aspx?doctype=5&filename=Compilations_NextTime_Shadows2.xml
External lessons
Additive and Subtractive Color in early color movies
http://www.widescreenmuseum.com/oldcolor/oldcolor.htm
Learning Standards
SAT subject test in Physics: Waves and optics
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color.
Massachusetts Arts Curriculum Framework: The Practice Of Creating
PreK- 4 Visual Arts Standards – Identify primary and secondary colors; predict and demonstrate the effects of blending or overlapping primary colors; demonstrate knowledge of making dark to light values of colors. Identify and use basic two-dimensional hollow and solid geometric shapes (circle, triangle, square, rectangle) and three-dimensional forms (sphere, pyramid, cube).
Grades 5-8 Visual Arts Standards – Create compositions that reflect knowledge of the elements and principles of art, i.e., line, color, form, texture; balance, repetition, rhythm, scale, and proportion. Demonstrate the ability to apply elements and principles of art to graphic, textile, product, and architectural design.
Massachusetts Arts Curriculum Framework
The Arts Disciplines: Visual Arts
PreK–12 STANDARD 2: Elements and Principles of Design
By the end of Grade 4: 2.1 Students will, for color, explore and experiment with the use of color in dry and wet media Identify primary and secondary colors and gradations of black, white and gray in the environment and artwork.
By the end of Grade 8: 2.7 Students will, for color, use and be able to identify hues, values, intermediate shades, tints, tones, complementary, analogous, and monochromatic colors. Demonstrate awareness of color by painting objective studies from life and freeform
abstractions that employ relative properties of color
Eclipses
Eclipses and the path of light: Geometric optics
How do we get a solar eclipse?
Details about this, and the Earth-moon system in general, are here:
Kaiserscience Earth-moon system.
But here are the basics:

Solar Eclipse via Shutterstock
How do we get a lunar eclipse?
First we need to know about the three types of shadows.
The umbra (Latin “shadow”) is the innermost, darkest part of a shadow.
This is where the light source is completely blocked.
The penumbra (Latin paene “nearly”) is where only a portion of the light is obscured.
An observer in the penumbra experiences a partial eclipse.
The antumbra (Latin ante, “before”) is where the occluding body appears entirely contained within the disc of the light source.
An observer here sees an annular eclipse, in which a bright ring is visible around the eclipsing body.
https://en.wikipedia.org/wiki/Umbra,_penumbra_and_antumbra
Here we see rays of light from the Sun, hitting the Earth. This happens 24-7.
Behind the Earth the three types of shadows always exist, 24-7.
If the moon passes through one of these regions, then we get one of these types of eclipses.
What are the conditions for a lunar eclipse?
Coding midterm
I. Write a sophisticated Scratch computer program, on your own, not using someone else’s code. You must first come see me with your idea, and then present quick updates, showing your progress.
Checkpoint 1 See me with your specific idea, by 5/30/17. 10 points.
Checkpoint 2: Show me the code you have each day in class. You need to be clearly explain how your code works. Your code should have many comment sections. By the time that finals come around, your program must be complete. If done well you can earn up to an additional 90 points.
II. Write a 4 page paper on one of the following topics.
No cover page. Upper left of the 1st page will have your name, my name/class, date and a title. Use 12 point Arial or Times New Roman font, double spaced, 1″ margins. You may add small diagrams and pictures, but they don’t count towards the length of your paper. MLA Works Cited is an additional page. You must use at least four sources of information, which must be cited in MLA format.
For these topics, most Wikipedia articles are acceptable sources, however, you may not use Wikipedia for more than 2 of your sources, and you must first show me the specific , so I can make sure that it’s Ok.
A) Computers don’t actually think. So how do they know what to do with the code we write? What goes on under the hood, so to speak? I’ve prepared many sources that you can use: How-a-computer-interprets-instructions
B) the development of computers and software: Choose 1 of these systems: the classic IBM-PC, Apple II, Apple Macintosh, Commodore Vic-20, or Commodore 64.
C) the development and programming of second generation classic video games. Choose 1 or 2 of these systems: Odyssey, Atari 2600 (aka Atari VCS), Magnavox Odyssey 2, Mattel Intellivision, Vectrex, and Colecovision. What kind of hardware was in these computers? How did they work? How were they programmed? In what language were they programmed? What was the software capable of?
D) the development and programming of third generation classic video games for neo-classic video games. Choose 1 or 2 of these systems: Sega Master System (aka the SMS), Nintendo (aka the NES or Famicon), Atari 7800. What kind of hardware was in these computers? How did they work? How were they programmed? In what language were they programmed? What was the software capable of?
E) the development and programming of fifth generation classic video games for neo-classic video games. Choose 1 or 2 of these systems: Sega Saturn, Sony Playstation (PSX 1), Nintendo 64. What kind of hardware was in these computers? How did they work? How were they programmed? In what language were they programmed? What was the software capable of?
Mirages
A mirage is a naturally occurring optical phenomenon in which light rays are bent to produce a displaced image of distant objects or the sky.
The word comes to English via the French mirage, from the Latin mirari, meaning “to look at, to wonder at”. This is the same root as for “mirror” and “to admire”.
In contrast to a hallucination, a mirage is a real optical phenomenon that can be captured on camera, since light rays are actually refracted to form the false image at the observer’s location.
What the image appears to represent, however, is determined by the interpretive faculties of the human mind. For example, inferior images on land are very easily mistaken for the reflections from a small body of water.
Mirages can be categorized as:
“inferior” (meaning lower)
“superior” (meaning higher)
“Fata Morgana”, one kind of superior mirage consisting of a series of unusually elaborate, vertically stacked images, which form one rapidly changing mirage.
Mirage. (2016, December 18). In Wikipedia, The Free Encyclopedia.
Problems
According to legend, Erik the Red sailed from Iceland and discovered Greenland after he had seen the island in a mirage. Describe how the mirage might have occurred.

Well, that answer from our textbook teacher editions, however true, isn’t very helpful. It’s not clear what we are looking at. Let’s look at a much better picture to see both the problem and the solution.
Problem: Erik the Red shouldn’t be able to see Greenland from where he is standing, on Iceland. Greenland is so far away that it is over the curve of the Earth (over the horizon.)
Solution:
The superior mirage, also know in northern polar regions as the arctic mirage — or in Icelandic, the hillingar effect — causes the light from distant objects to be optically refracted downward
Thus it becomes possible for objects lying beyond the normal horizon to be seen.
(They even appear, at times, to rise up over the horizon, a condition known to mariners as looming, and look much closer in distance.)
Fata Morgana Mirage in Greenland, 1999, by Jack Stephens

SEE BELOW FOR THE FAMOUS MOBY DICK MIRAGE

The arctic mirage, on the other hand, occurs when the light rays are refracted downward by cold, dense air near the earth into an arc bending toward the observer. (In the diagrams accompanying this article, the dark lines indicate the actual light ray path and the white dashed lines the path our mind thinks it sees.)
The refractivity of air — a measure of the air’s ability to bend the path of light rays — is dependent upon its density, and the density of air is inversely related to its temperature (decreasing as temperature increases). The atmospheric conditions for producing the arctic mirage occur when cool air adjacent to the surface underlies warm air. When the air temperature increases with altitude, the condition is known meteorologically as a temperature inversion.
When the temperature of the lower atmosphere increases with altitude at a rate of 11.2 C° per 100 metres (6.0 F° per 100 ft), the refractive capacity of the air is great enough to cause the path of light rays to bend in an arc equal to the curvature of the Earth.
This curvature can present an observer with the image of a flat horizon receding to infinity. A temperature gradient greater than 11.2 C° per 100 m causes light ray paths to exceed the curvature of the Earth, and thus the horizon would appear to be raised upward giving the Earth’s surface a saucer-shaped appearance.
Under this latter condition, images of objects located at or below the normal optical horizon, such as mountains, glaciers, cliffs or sea-ice rise (loom) into the field of vision, overcoming the normal visual restrictions of the curvature of the Earth.
The normal viewing distance at the surface of the earth depends upon the height of the object being observed and the height of the observer. Disregarding atmospheric effects on light rays, the curvature of the earth restricts the distance one can see from the surface.
For example, a beach or small iceberg rising 3.0 to 3.7 m (10 to 12 ft) above the sea surface can be seen from the surface at a distance of no more than 19.2 km (12 miles) through a clear, normal atmosphere.
A mountain peak of 914 metres (3,000 feet) would disappear at 115 kilometres (72 miles) distant, one 1520 m (5,000 ft) tall at 150 km (94 miles).
The maximum viewing distance under arctic mirage conditions, on the other hand, is limited only by the light absorption of the atmosphere. Near sea level, the transmission of light is generally of sufficient quality to enable the naked eye to potentially see objects at a distance of up to 400 km (250 miles).
However, when the refracting layer is at the upper boundary of a very deep cold layer, the thinner air may permit more light to be transmitted, thus making visibility in excess of 400 km possible.

Under arctic mirage conditions, instances of atmospheric visibility extending 320 km (200 miles) have been reported. In 1937 and 1939, W.H. Hobbs documented several occasions during which objects were sighted at distances well in excess of those possible under normal viewing conditions.
Answer text from The Arctic Mirage. Aid to Discovery. The Weather Doctor.
Moby Dick illusion
James Rickards writes
One famous literary description of a Fata Morgana occurs in Chapter 135 of Herman Melville’s masterpiece, Moby Dick. As Ahab is pulled overboard, and the White Whale rams the Pequod, Melville writes:
“The ship? Great God, where is the ship? Soon they through dim, bewildering mediums saw her sidelong fading phantom, as in the gaseous Fata Morgana.”
But, of course the ship was sinking, the vision was an illusion.

Amazing examples
A Ship Floating In Mid-Air At A Scottish Golf Tournament?
Images from Why Was There A Ship Floating In Mid-Air At A Golf Tournament? BuzzFeed
Just like the above mentioned mirages!

Enter a caption
image: Tom Phillips/BuzzFeed/ilyast/syntika/Thinkstock
Floating boats and islands
Video
Island and fishing boat mirage
Fata Morgana Mirage at Cocoa Beach, FL!
https://www.youtube.com/watch?v=VcEn3jb3oq4
Lake Superior Marquette, MI 05.23.15 – first scene is real time, freighter in to Marquette, second is timelapse, Granite Island looking like a lava lamp
https://www.youtube.com/watch?v=xJfJTdy2Ge8
External links
An Introduction to Mirages, Andrew T. Young
Fata Morgana between the Continental Divide and the Missouri River
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.
A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
Core Idea PS4: Waves and Their Applications in Technologies for Information Transfer
When a wave passes an object that is small compared with its wavelength, the wave is not much affected; for this reason, some things are too small to see with visible light, which is a wave phenomenon with a limited range of wavelengths corresponding to each color. When a wave meets the surface between two different materials or conditions (e.g., air to water), part of the wave is reflected at that surface and another part continues on, but at a different speed. The change of speed of the wave when passing from one medium to another can cause the wave to change direction or refract. These wave properties are used in many applications (e.g., lenses, seismic probing of Earth).
The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing. The reflection, refraction, and transmission of waves at an interface between two media can be modeled on the basis of these properties.
All electromagnetic radiation travels through a vacuum at the same speed, called the speed of light. Its speed in any given medium depends on its wavelength and the properties of that medium. At the surface between two media, like any wave, light can be reflected, refracted (its path bent), or absorbed. What occurs depends on properties of the surface and the wavelength of the light.
SAT Subject Area Test in Physics
Waves and optics:
- 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
Also see Benchmarks: American Association for the Advancement of Science












