Directions: Reflection is both a part of science and a personal practice. The questions that follow will help students take notes, brainstorm ideas and test their thinking on reflection-related concepts in order to be more actively engaged in class discussions. Start off the discussion by asking the entire class to answer Questions 1 and 2. Allow students some time to think about answers to the questions, then have students share their answers aloud. You may want to start the class with a reflective practice, such as deep breathing or even a few yoga stretches. The other option is to allow a student to lead one of his or her favorite reflective practices, though you probably want to vet the practice before the start of class. After completing this introduction, allow students time to find and read articles related to the sections you’d like the students to complete.

 1. What is reflection? How can reflection be useful?

In physics, reflection is when a wave (light, sound, water wave, etc.) bounces off a surface or a boundary between two materials. In many cases, a reflection can bounce back an image of whatever initially produced the wave (just as a mirror shows you your image). Mirrors and other reflective materials show up in many technologies, such as space shuttles and some solar-powered devices.  

Instead of looking at your mirror image or other bouncing waves, reflection can also mean looking at your own thoughts, feelings, actions and accomplishments. It can be useful to carry out that sort of reflection periodically, in order to take stock of how far you have come, which direction you would like to go next and what aspects of yourself still need the most work.

2. How much reflective thinking have you done in the past? What methods or practices did you use?

Student answers will vary. Also see the Resource Sheet on Reflective Practice Tips and Tricks at the end of this section.

Scientific Reflection

1. What is wavelength?

Wavelength is the distance of one complete cycle of the wave. If the wave is a transverse wave wiggling up and down, one wavelength includes one hump up and one hump down, or the distance between consecutive wave crests or troughs. If the wave is longitudinal, one wavelength includes a region of compression and a region of stretching. Wavelength is typically measured in meters (m). 

2. What is the frequency of a wave?

Frequency is how many complete cycles of a wave (one cycle being one wavelength) zip by per second. It is measured in Hertz (Hz), or cycles per second. 

3. What is the velocity of a wave?

Velocity is how fast a wave is moving, or the distance traveled by the wave per second. It is typically measured in meters per second (m/s). 

4. What is constructive interference? What is destructive interference?

The highest point on a transverse wave is called the peak, the lowest point is the trough and the amplitude is the vertical distance from the peak or trough of a wave to the middle equilibrium point, or node, where the wave transitions from peak to trough.

Two waves undergo constructive interference when peaks align, and the amplitude of the resulting wave is the sum of the amplitude from each aligned peak. Destructive interference is when peaks of one wave align with the troughs of another wave. The amplitude of the resulting wave is the amplitude of the peak minus the amplitude of the trough. If identical waves are aligned so that the peak of one wave matches the trough of another, the waves will completely cancel.

5. How are mirrors made?

Most mirrors are made of polished metal, which reflects light very well, covered by glass or sometimes plastic. The covering keeps oxygen in the air from tarnishing the metal surface.

6. What determines the direction that light reflects from a mirror?

The direction that light reflects from a mirror depends on the angle at which light strikes that mirror. The angle of incidence of the light is measured relative to a vector that is perpendicular to the mirror’s surface. The angle of reflection (the angle of light leaving the mirror, relative to a vector that is perpendicular to the mirror’s surface) is equal to the angle of incidence. Thus, light striking the mirror at 90 degrees (head on) reflects straight back at 90 degrees. If light traveling from the left hits a mirror at a 10-degree angle of incidence, it will be reflected toward the right at a 10-degree angle of reflection.

7. The Science News article “Perfect mirror debuts,” published 7/10/2013, and the accompanying Science News for Students article “Perfect reflections,” published 7/18/2013, describe a new technology for creating a perfect optical reflection. What information do both of those articles report?

Even a well-made normal mirror absorbs a small amount of the light that strikes it, so that a bit less than 100 percent of the light is actually reflected by the mirror. That loss might sound insignificant, but it is important to maximize the amount of reflected light in some applications. Scientists found a way to create a perfect mirror that reflects all of the light that strikes it and absorbs none, at least for light of a particular wavelength (color) striking the mirror at a particular angle.

The scientists created regularly spaced holes in the surface of the mirror in order to take advantage of the phenomena of constructive and destructive interference. Light waves that travel through those holes destructively interfere with each other. That means effectively no light penetrates the mirror and the remaining light is reflected. The correct hole spacing to create destructive interference depends on the wavelength and the angle of incoming light, which is why this method does not work for all wavelengths and angles.

8. What facts did you learn from only the Science News article? What was included only in the Science News for Students article?

Science News: John von Neumann first proposed this approach in 1929. The same technique might work with sound waves or with water waves.

Science News for Students: Definitions of crystal, photonic crystal and laser. 

Historical Reflection

Note: Students with access to a computer can do additional research as needed.

1. Most of the famous scientists, engineers and mathematicians we hear about, especially from the early history of science, were men. Give a few examples of women who have made significant contributions to science, math and/or engineering. Feel free to explore the resources listed below.

General resources:

Margaret Alic, Hypatia’s Heritage (1986).

Rachel Ignotofsky, Women in Science (2016).

G. Kass-Simon and Patricia Farnes (editors), Women of Science (1990).

Sharon McGrayne, Nobel Prize Women in Science (2001).

Some examples in chronological order:

Hypatia of Alexandria (circa 360–415) was a philosopher, astronomer and mathematician, and the last curator of the ancient Library of Alexandria.

Caroline Herschel (1750–1848) discovered several comets and compiled a star catalog. She also made astronomical observations with her brother William Herschel (the discoverer of Uranus).

Mary Anning (1799–1847) discovered an ichthyosaur skeleton, one of the first skeletons from the age of the dinosaurs to be identified and analyzed, when she was 12 years old. She later found and studied many other important fossils.

Ada Lovelace (1815–1852) was a mathematician who made the first detailed proposals for computer programming. She worked with Charles Babbage on a mechanical computer design.

Marie Curie (1867–1934) and her daughter Irène Joliot-Curie (1897–1956) were early pioneers of nuclear physics, together with their husbands. Both Marie and Irène won a Nobel Prize in chemistry, and Marie shares a Nobel Prize in physics with her husband.

Henrietta Leavitt (1868–1921) discovered Cepheid variable-intensity stars and showed that they could be used as beacons to measure distances in the universe. She died in obscurity before Edwin Hubble used Cepheid stars to demonstrate the expansion of the universe, for which he won many prizes. For more information, see: George Johnson, Miss Leavitt’s Stars (2005).

Barbara McClintock (1902–1992) conducted some of the earliest studies on DNA chromosomes, and ultimately won a Nobel Prize for her work.

Mary G. Ross (1908–2008) was an engineer who was one of the 40 original engineers of Skunk Works, and worked for Lockheed Martin studying satellites and space travel. 

Maria Goeppert Mayer (1906–1972) was a physicist who helped to develop the shell model for the structure of the atomic nucleus, for which she won a Nobel Prize. She also helped to develop the first U.S. nuclear fission (atomic) and fusion (hydrogen) bombs.

Rosalind Franklin (1920–1958) used X-rays to measure the structure of DNA. Without her permission, her data on the structure of DNA was analyzed and reported by Francis Crick and James Watson, who, along with Franklin’s boss Maurice Wilkins, won a Nobel Prize for the results. Franklin died of cancer about four years before the trio won the Nobel Prize.

Mary Jackson (1921–2005) was a mathematician and aerospace engineer at the National Advisory Committee for Aeronautics (NACA). She authored many papers on how the boundary layer of air around airplanes behaves. In 1979 she left engineering to become Langley’s Federal Women’s Program Manager, working to support the hiring and promotion of women within the National Aeronautics and Space Administration (NASA).

2. Do you think these scientific pioneers receive the recognition that they deserve? Why or why not?

Student answers will vary.

3. What barriers have these scientists faced?

There are many institutional and social barriers that have hampered women from receiving a scientific education or pursuing a scientific career. It has been difficult for even the most scientifically and politically talented woman to surmount those barriers. Having a strong male advocate within academia often helped to reduce barriers for some of the first women to successfully enter the system. In many cases, that strong advocate was a father, brother or husband who was already an accepted part of the scientific educational and research system. (For example, Pierre Curie refused to accept the 1903 Nobel Prize in physics unless the prize was also awarded to his wife, Marie Curie, in proper recognition of her work.) As the institutional and social barriers gradually lowered over time, it became somewhat easier for women to successfully enter academia even if they did not have a personal advocate. There are probably many talented women we have never heard of because of institutional and social barriers they faced.

4. What scientist, mathematician, engineer or medical doctor do you find most inspirational? Why?

Student answers will vary.

5. What are some similarities or differences between your interests and those of the person you find most inspirational?

Student answers will vary.

6. What are some similarities or differences between your education and that of the person you find most inspirational?

Student answers will vary.

7. What are some similarities or differences between your career goals and those of the person you find most inspirational?

Student answers will vary.

8. What are some similarities or differences between obstacles that you have faced and those faced by the person you find most inspirational?

Student answers will vary.

Self-Reflection and Practices

Please note that student answers will vary for all of these questions.

1. How did this school year go? Explain.

2. What have you accomplished over the past year that you are proudest of?

3. What have you learned over the past year that you are proudest of?

4. What challenges have you overcome over the past year?

5. What specific aspirations or goals do you have for the next year?

6. How could you measure your progress toward those goals?

7. What are your reflections on your academic achievement so far? List both positive personal accomplishments and areas of personal improvement.

8. What are your reflections on your personal characteristics? List both positive personal accomplishments and areas of personal improvement.

9. Are there benefits to reflection? If so, what are they?

10. Do you practice reflection daily, weekly, monthly? Explain.

11. What techniques for reflection could be useful on a regular basis?