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#### Mirror, Mirror on the Wall: Angles of Reflection

When you look at an object in a mirror, what you see is the reflection of light from that object. Reflection involves two types of light rays: the incoming, or incident, ray and the outgoing, or reflected, ray. The angle between the incident ray and an imaginary perpendicular line drawn to the surface of the mirror is called the angle of incidence. The angle between the reflected ray and the perpendicular is called the angle of reflection. According to the law of reflection, light is always reflected at the same angle that it arrives at a surface. In other words, when light comes into contact with a mirror, the angle of reflection equals the angle of incidence.

Required Materials

• Science notebooks
• Mirror
• Paper

What will the students do?

Students will mount the mirror, which should be covered with a piece of paper, flat on a wall at eye level. Making sure to use the mirror as a centerline, have students lay a 2 to 3 meters length of masking tape on the floor, extending out from, and perpendicular to, the wall.

Students will then work in pairs using the student page as a guide. They will be challenged to predict where two people must stand so each can see the other's reflection in the mirror. Each pair will discuss and agree on the places where they think they must stand. They will draw diagrams in their science notebooks to show the places they have selected.

Once students have determined where they will stand, they remove the paper from the mirror and test their predictions. Pairs of students will continue doing this until they have found and marked the places where they must stand to see both reflections in the mirror.

Interactive Java Tutorial
 Angles of Reflection Explore how light reflects off of a mirror at different angles.

Activity Extensions

Mathematics - Show students how to use protractors to measure angles. Then, have students design and construct large protractors out of cardboard to measure their angles of incidence and reflection. Ask them to draw and record their results in their science notebooks. Each team of students should be able to explain to another group how they constructed the protractors and how they used the tools to measure the angles.

Reading - Either read aloud or have students read the fairy tale Sleeping Beauty or the book Through the Looking Glass before they go onto the narrative writing prompt. Discuss ahead of time how mirrors are used in both stories and how the use of mirrors allows characters to see and do things they could not do in a real world.

Writing - Use the following as a narrative writing prompt: In the fairy tale Sleeping Beauty and in the story Through the Looking Glass, mirrors are magical. Use your imagination and think about how mirrors could be used in magical ways. Now write a short story about your magical mirror.

Game - Discuss with students how light reflects off a mirror like a ball bounces off a surface. Then have them think about how a basketball bounces off the backboard of a basketball goal. Encourage them to make up a game in which they use flashlights to reflect light off of a mirror onto a goal or target. Have them write instructions and develop diagrams to help explain their games. Put them together in small groups so they can try playing the games they designed.

Historical Vignette: Euclid and His Students

The ancient Greek scientist and mathematician Euclid, who lived 2300 years ago in Alexandria, Egypt, was one of the first to explain how light reflects off of a mirror. Though much of his time was invested in the workings of light, Euclid is most known for his mathematical presence, specifically in geometry.

Very little is known about Euclid's personal life, but he did start a school in Alexandria and worked hard to help his students learn. The young King of Egypt was once one of his students. One day, the King asked Euclid if there was an easier way for him to learn geometry than by studying. Euclid answered, "There is no royal road to geometry" and sent the young King off to study.

There is another story about Euclid in which a student wanted to know what he was going to get for learning geometry. Euclid was concerned that this student felt that he needed to receive something for learning. So Euclid called his assistant and told him to give the student a coin, since "he must make gain out of what he learns."

Research - Euclid was not the only scientist that contributed to our understanding of light and reflections. In the 1100s the Arab scientist Alhazen studied the reflection of light and discovered the law that describes exactly what happens to a ray of light when it strikes a surface and then bounces off of it. Using a variety of print and electronic media, students can research and write about the discoveries of Euclid and Alhazen.

Artist Vignette: Leonard da Vinci

Leonardo da Vinci was a great artist and scientist that lived from 1452 to 1519, during a time called the Renaissance. He was one of the greatest painters of the period. The Last Supper and the Mona Lisa are two of his best-known paintings.

Da Vinci was also a great engineer and inventor. He designed buildings, bridges, canals, forts, and war machines. He was fascinated by birds and flying and drew designs of fantastic flying machines, keeping huge notebooks of his designs and ideas.

In his notebooks, da Vinci wrote using "mirror writing," writing that went backwards from right to left, instead of from left to right. In order to read his writing normally, you must place a mirror beside the writing and read the reversed image in the mirror. No one knows why he wrote this way. Some people believe he was trying to keep people from stealing his ideas. Others point out that he was left-handed which made it easier for him to write from right to left.

To this day, people enjoy looking through the fantastic notebooks of Leonardo da Vinci. You can find many books in libraries with pictures of his notebooks and paintings. There are also many Internet sites with more information about da Vinci, his art, his inventions, and his mirror writing.

Activity - After reading the vignette aloud, challenge students to write their names backwards. Have students use mirrors to check to see if they correctly reversed the letters. Students can also use the mirrors as they are writing and write messages to their parents or friends. After looking at reproductions of da Vinci's notebook pages, challenge students to draw designs of fantastic flying machines or space ships. Have them label their designs using mirror writing.

 Grades K-2 Standards Science: SC.B.1.1.2, SC.H.1.1.1, SC.H.1.1.2, SC.H.1.1.3, SC.H.1.1.4, SC.H.1.1.56, SC.H.3.1.1 Mathematics: MA.B.1.1.1, MA.B.1.1.2, MA.B.2.1.1, MA.B.3.1.1, MA.B.4.1.2, MA.C.1.1.1, MA.C.2.1.1, MA.C.2.1.2, MA.C.3.1.1 Social Studies: SS.A.2.1.3 Language Arts Arts: LA.A.2.1.5, LA.B.2.1.1, LA.B.2.1.2, LA.B.2.1.4 Visual Arts: VA.A.1.1.1, VA.C.1.1.1, VA.C.1.1.2, VA.E.1.1.1

 Grades 3-5 Standards Science: SC.B.1.2.2, SC.H.1.2.1, SC.H.1.2.2, SC.H.1.2.3, SC.H.1.2.4, SC.H.2.2.1 Mathematics: MA.A.4.2.1, MA.B.2.2.1, MA.B.2.2.2, MA.B.4.2.2, MA.C.1.2.1, MA.C.2.2.1, MA.C.2.2.2, MA.D.2.2.2 Social Studies: SS.A.2.2.1, SS.A.2.2.5 Language Arts: LA.B.2.2.1, LA.B.2.2.3, LA.B.2.2.4, LA.B.2.2.5, LA.B.2.2.6 Visual Arts: VA.A.1.2.1, VA.C.1.2.2