Core Unit III: Light
B. Reflection

2). Plane Mirrors

Key Concepts

A plane mirror is a planar reflecting surface, on which specular (regular) reflection is observed.

A virtual image is formed by a plane mirror. The rays reflecting from the mirror appear to have originated from the location of the virtual image.

On a diagram, a virtual image is usually depicted by a broken (dotted) arrow.

A real image (formed by other kinds of optical devices) can be focused on a screen, whereas a virtual image can not.

On a diagram, a real image is usually depicted by a solid arrow.

The image in a plane mirror is located as far behind the mirror as the object forming it is in front of the mirror. It is the same size as the object. (magnification = +1)

magnification (m)	=	height of image
		----------------
		height of object
	=	Hi
		---
		Ho
	= -	di
		---
		do

where d_i is the distance from the image to the mirror, and d_o is the distance from the object to the mirror. (Note that some resources use the symbols p and q instead of d_o and d_i respectively.)

The mirror equation, for a plane mirror, as described in the next section, yields

R = and f =

, so

, d_i = - d_o and m = +1

R is the radius of curvature and f is the focal length.

The image formed in a plane mirror is erect but laterally inverted. (Lateral inversion is also referred to as "left-right reversal, "left-right inversion" or even "perverted" in different resources.)

In any optical system there are four important image characteristics which need to be considered: magnification, attitude (erect or inverted), type (real or virtual), and position.

Ray diagrams are an important aid used in geometric optics.

A ray diagram is used to trace the path of rays through an optical system.

A ray diagram and terminology for reflection

Ray diagrams should always be labelled properly. They should also be drawn neatly, accurately, and to some appropriate scale.

The scale used on a ray diagram should always be stated explicitly.

Ray diagrams give a close approximation to numerical solutions to problems in optics. Ray diagrams are useful for verification, and to illustrate important ideas. They are also used to derive formulas and to develop more complex methods of optical analysis.

A ray diagram can be used to determine the characteristics of an image formed in a plane mirror, as well as in other optical systems.

A solid line on a ray diagram is used to illustrate the path of a light ray.

Arrows are used on the solid lines to show the direction of propagation of light.

By convention, incident rays are usually depicted on a ray diagram as travelling from left to right.

A dotted line is used as a construction line. Light rays do not travel along those dotted lines.

Lenses and mirrors are shown in profile on ray diagrams.

When two plane mirrors are joined at a 90^o angle, three virtual images are produced. Geometrically, the object and the three images lie at the corners of a rectangle whose centre is the line of intersection of the mirrors. Two reflections occur to form the central image.

Two mirrors placed at an acute angle to one other produce a kaleidoscopic effect, with multiple images formed.

For two mirrors placed at any angle, the number of images formed by the mirrors can be determined by:

where is the angle between the mirrors and N is the number of images formed.

If = 0^o (parallel mirrors) N approaches infinity. (This effect is sometimes seen with parallel mirrors in hairdressing salons or barbershops.)

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: real image, virtual image, plane mirror, magnification, ray diagram.

2. Identify the characteristics of an image formed by a plane mirror.

3. Distinguish between a real and a virtual image.

4. Identify some optical systems which produce either a real or a virtual image.

5. Draw ray diagrams neatly, accurately, and to some appropriate scale.

6. Apply the correct use of solid and dotted lines on ray diagrams.

7. Interpret solid and dotted lines on ray diagrams.

8. Label ray diagrams correctly, using conventional symbols.

9. Determine appropriate scales to use when drawing ray diagrams.

10. Apply the magnification formula and the mirror equation in problem solving.

11. State the four important image characteristics which need to be considered for any type of optical system.

12. Recognize and explain the importance of ray diagrams in geometric optics.

13. Demonstrate an understanding of important principles of drawing ray diagrams.

14. Draw ray diagrams for analysis and for solving problems dealing with optics.

15. Recognize the combined use of ray diagrams and equations in solving problems related to optics.

16. Use ray diagrams, along with other experimental or theoretical methods, to determine the characteristics of an image in an optical system.

17. Describe the location and number of images formed by two perpendicular plane mirrors.

18. Suggest some applications of multiple images formed by more than one mirror.

Teaching Suggestions, Activities and Demonstrations

1. Construct a kaleidoscope which allows the angle between the mirrors to be adjusted. Describe what happens to the patterns observed when the angle between the mirrors changes.

2. Experimentally investigate the characteristics of images formed in a plane mirror. Illustrate using ray diagrams or explain why a plane mirror produces a virtual image.

3. A good idea for drawing straight lines on a blackboard is to use a carpenter's chalk line. They come with blue or red chalk. They can save some hassles when drawing ray diagrams. Hold both ends of the string down firmly in place, and have an assistant snap the chalk line to leave the mark. Instead of a chalk line, you could even use regular string and coat it with chalk dust.

4. Suggest practical applications which illustrate the lateral inversion of an image in a plane mirror.

5. Emphasize the distinction between lateral and vertical inversion. They are confused easily.

6. Straddle a full-length mirror sideways, so that students see one leg in front of the mirror, while the other leg is behind the mirror out of their view. The mirror should be tall enough so that it reaches from the floor to your crotch. While balancing on the rear leg, out of the view of the class, slowly raise the leg that is visible to them and lean forward slightly. The reflection in the mirror creates the illusion that the rear leg is also being lifted, allowing you to "levitate" before their very eyes. Wearing a cape, having a fan blowing over the cape to produce a breeze, and holding your arms outstretched may create an illusion of flight. This demonstration is likely to be a success if it is set up carefully beforehand.

   A follow-up might include a discussion of how mirrors are used to produce theatrical effects and optical illusions.

7. Show students how to use ray diagrams as a means of verification for numerical solutions to problems.

8. Perform an activity to observe the number of images formed by two mirrors placed at 60°, 45°, and 30° angles to one another. Calculate the number of images formed by two mirrors placed at an acute angle to one another. Confirm that the number of images observed and calculated agree with one another.