Lesson C5: Mathematics of Light

Key Ideas     Unit Checklist

  Video Lesson

Light reflects off mirrors in predictable patterns. Watch this video to learn more about the mathematics of light.

 
 

  Lesson C5: Mathematics of Light


Figure C.2.5.1 – Convex side mirrors produce smaller virtual images.

Figure C.2.5.2– Words on emergency vehicles are sometimes printed backwards so they can be read in car mirrors.


Figure C.2.5.3– Convex mirrors bulge outward, reflecting a larger field of view.
Reading and Materials for This Lesson

Science in Action 8
Reading: Pages 194–199

Materials:
Two milk cartons (1-litre size, empty and clean), sharp scissors, two small flat pocket mirrors (preferably square), tape (packing or duct), small toy, protractor.

Vehicle Mirrors

Mirrors are an important safety feature on vehicles. Vehicle mirrors point backwards, which allows drivers to observe their side and rear surroundings. Mirrors allow drivers to see other vehicles without taking their eyes off the road for more than a quick glance into the mirror. Many emergency vehicles are labelled with words printed backwards, so they are readable in a rearview mirror.

In North American vehicles, the driver’s side mirror is flat. It creates an image the same size as the original object. However, the passenger side mirror curves outward slightly for a wider field of view. An mirror that curves outward is called a convex mirror. Convex mirrors only produce virtual images that cannot be projected onto a surface. Images in convex mirrors are smaller than the real life object. For this reason, “Objects in mirror are closer than they appear” is written on some car mirrors.

  Try It! 


Multiple Reflections

Try this experiment to observe how light can reflect multiple times in mirrors.

Materials: 
  • Two small flat mirrors
  • Object smaller than the mirrors, like a small toy
  • Protractor

Instructions:

  1. Place the toy on a flat surface.

  2. Place both mirrors, facing you, about 5 centimetres beyond the small toy. Hold the mirrors vertically, side by side, at a 180 degree (straight) angle. The toy should be in the middle. What do you observe in the mirrors?

    Download a copy of this protractor if you want help with forming the angles. Place the toy on the protractor, between the two mirrors. Line up the mirrors along the base line. In Steps 3 and 4, you will move one mirror to the angle lines.

     

     


  3. Angle the mirrors toward you, so they form a 120 degree angle. Use the protractor to measure the angle. Have someone help you hold the mirrors if necessary. Make sure the toy is in the middle of the mirrors. What do you observe? Count the number of mirror images that you see.

  4. Repeat step 3 for mirror angles of 90 degrees, 60 degrees, 45 degrees, and 30 degrees.

  5. Watch this video to see this a similar experiment and its results:


 
 

Questions: 

Think about the following questions very carefully. Then, type or write your answers. After you have your answers, click the questions for feedback.


As the angle between the two mirrors became smaller, more images of the toy were produced in the mirrors.
Reflected light forms images in mirrors. As the angle decreased between the two mirrors, light reflected off one mirror and hit the second mirror, forming an additional image. At small angles, light rays made many back-and-forth reflections in the mirrors to create multiple images.

Lesson Activity

Mirror Image Simulation

 Problem:

Try this online simulation to learn how concave mirrors produce different images.

Download:
DOWNLOAD this document. It provides a space for you to write answers to the analysis questions later in this activity. It also provides a chart for you to record your observations.
  


Instructions:

  1. Click here to open the simulation.

  2. Play with the simulation to see what happens when you move the torch to different positions. Click and drag on the torch’s cross-arrow button to move it forward and backward. Click and drag on the torch’s square button to change its size and flip it upside down. Click on the “show rays” and “show grid” buttons to see what happens.

  3. Adjust the torch’s position to create the images listed in the chart below. A virtual image forms behind the mirror and cannot be projected onto a screen. A real image forms in front of the mirror and can be projected onto a screen.

  4. Record the position of the torch relative to the focal point (F) and the centre of curvature (C).

  5. Record the orientation of the torch as right side up or upside down.

  6. Record the height of the torch.
Analysis Questions:

Think about the following questions very carefully. Then, type or write your answers. When you have your answers, click the questions for feedback.


When the torch was between the focal point and mirror, a virtual image formed. The virtual image was always larger than the actual torch, and the image always had the same orientation as the torch.
When the torch was between the focal point and the centre of curvature, a real image formed beyond the centre of curvature. The real image was always larger than the actual torch, and the image always had the opposite orientation as the torch.
When the torch was beyond the centre of curvature, a real image formed between the centre of curvature and the focal point. The real image was always smaller than the actual torch, and the image always had the opposite orientation as the torch.
A concave mirror produces an image the same height as the torch at the centre of curvature. The image has the opposite orientation to the actual torch.

  Connections 


Figure C.2.5.4– A periscope uses mirrors or prisms to reflect light.

Figure C.2.5.5– Submarine periscopes allow the crew to see above the water’s surface.


Figure C.2.5.6– Periscopes have been used as a tool in military operations.
Connections – Technology
>> The Periscope

Some scientific inventions have controversial purposes. For example, the use of scientific inventions in the military can be controversial, because people have different opinions about fighting wars.

The periscope is an invention from the 1800’s that is still used in military machinery. Early periscopes used mirrors to reflect an image downward. Mirror periscopes were attached to guns and binoculars in both World Wars to allow soldiers to see above trenches without exposing their bodies to danger. Periscopes are also attached to submarines, to allow people underwater to see above the surface. Modern periscopes use lenses to create images, similar to telescopes.

  Try It! 


Make a Periscope

Try this experiment to make a simple mirror periscope. 

Materials: 
  • Two empty and clean 1-litre milk cartons
  • Sharp scissors
  • Two small flat pocket mirrors (preferably square)
  • Packing or duct tape
  • Protractor

Take care with scissors; don't cut yourself or anyone else!
Instructions:

  1. With the scissors, cut the top and the bottom off a milk carton.


  2. From the bottom of the milk carton, make a cut that is the same height as the mirror. Make an identical length cut on the three other bottom edges of the milk carton.

  3. The cut edges form flaps on the bottom of the milk carton. Fold back two flaps on opposite sides of the milk carton.

  4. Cut off one of the flaps along its fold.

  5. Tape a mirror securely to the inside of the remaining folded flap.

  6. Repeat steps 1 to 5 for the other milk carton.

  7. Arrange the two milk cartons so that their uncut sides touch. Turn one milk carton to have its mirror flap facing down. Turn the other milk carton to have its mirror flap facing up. Tape the two cartons together around their uncut sides, to form a long box.

  8. On one end of the long box, fold the mirror flap inward at a 45 degree angle, to face the hole. Cut off the extra triangles on the sides, and tape the mirror flap to the sides of the box. Repeat for the other end of the periscope.

  9. Hide underneath a table and extend your periscope out above the tabletop. Look at the mirror in the bottom end of your periscope. What do you observe?

  10. Watch this video to see a similar experiment and its results:

 
 

Questions: 

Think about the following questions very carefully. Then, type or write your answers. After you have your answers, click the questions for feedback.


Light rays from above travel into the top mirror, which then reflects the light rays into the bottom mirror. The bottom mirror reflects the light rays, forming an image of the elevated object that you can see from a lower position.
When the upper mirror is placed at a 45° angle, light rays hit this mirror at a 45° angle. Due to the Law of Reflection, the light rays are reflected at a 45° angle, which sends them straight down the long box to the lower mirror. When the lower mirror is also placed at a 45° angle, light rays hit this mirror a 45° angle. Due to the Law of Reflection, these light rays are reflected at a 45° angle, which sends them horizontally out the periscope to your eye.
Sharing:

Congratulations on completing this activity! How did your periscope turn out? Consider sharing your completed periscope in the course Sharing Forum. Take a photo of it and post it; your teacher and other students would be interested in seeing how your periscope turned out!


Look in the Mirror

Have you looked in a mirror today? We use mirrors to view objects that we can’t otherwise see. We also use mirrors to reflect light in different technologies. What are mirrors made from? Why do we sometimes use curved mirrors instead of flat mirrors?

Click here to Explore with Elsie about different types of mirrors.



  Make sure you have understood everything in this lesson. Use the Self-Check below, and the Self-Check & Lesson Review Tips to guide your learning.

Unit C Lesson 5 Self-Check

Instructions


Complete the following 6 steps. Don't skip steps – if you do them in order, you will confirm your understanding of this lesson and create a study bank for the future.

  1. DOWNLOAD the self-check quiz by clicking here.

  2. ANSWER all the questions on the downloaded quiz in the spaces provided. Think carefully before typing your answers. Review this lesson if you need to. Save your quiz when you are done.

  3. COMPARE your answers with the suggested "Self-Check Quiz Answers" below. WAIT! You didn't skip step 2, did you? It's very important to carefully write out your own answers before checking the suggested answers.

  4. REVISE your quiz answers if you need to. If you answered all the questions correctly, you can skip this step. Revise means to change, fix, and add extra notes if you need to. This quiz is NOT FOR MARKS, so it is perfectly OK to correct any mistakes you made. This will make your self-check quiz an excellent study tool you can use later.

  5. SAVE your quiz to a folder on your computer, or to your Private Files. That way you will know where it is for later studying.

  6. CHECK with your teacher if you need to. If after completing all these steps you are still not sure about the questions or your answers, you should ask for more feedback from your teacher. To do this, post in the Course Questions Forum, or send your teacher an email. In either case, attach your completed quiz and ask; "Can you look at this quiz and give me some feedback please?" They will be happy to help you!

Be a Self-Check

Superhero!



Self-Check Quiz Answers

Click each of the suggested answers below, and carefully compare your answers to the suggested answers.

If you have not done the quiz yet – STOP – and go back to step 1 above. Do not look at the answers without first trying the questions.

Due to the Law of Reflection, incoming light at a 45-degree angle will reflect at a 45-degree angle. The mirror will reflect light rays directly upward into the camera body.
Parking garage mirrors are curved convex mirrors. These mirrors can collect light from a larger area to create images with a larger field of view, like around corners.
Concave mirrors can form real images in front of the mirror. Real images can be projected onto a screen. Convex mirrors only form virtual images behind the mirror. You must look into the mirror to see the image formed by a convex mirror.
Images of objects reflecting in a mirror follow the Law of Reflection. Even if you cannot see your own image in the mirror, light rays travelling from other objects will strike the mirror and reflect off at the same angle, toward your eyes.
A makeup mirror is a curved concave mirror. These types of mirrors form larger virtual images when the object is between the focal point and the mirror.