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Lesson 1 of 7

Light: Mirrors and Lenses · Lesson 1 of 7

What Are Spherical Mirrors?

“Discover how the shape of a reflecting surface changes the mirrors we use.”

Learning Objectives

• Distinguish plane mirrors from spherical mirrors. • Identify concave and convex mirrors by their reflecting surfaces. • Investigate the two sides of a shiny spoon without assuming that every image is the same. • Read the shaded side in a schematic mirror drawing. • Explain the imaginary-sphere model and the role of a reflective coating.

A familiar reflection can become surprising

Imagine visiting a science centre with Meena. In one curved mirror her face looks larger, while her brother, standing farther away, looks upside down. Another mirror shows a smaller version of her. Nothing has happened to their actual faces: the mirrors are changing how light reaches their eyes.

A plane mirror has a flat reflecting surface. At this level you already know that its image is erect, meaning upright, and the same size as the object. An object is the person or thing placed in front of a mirror; its image is the appearance you see in the mirror. Curved reflecting surfaces can produce a different appearance, which is why we must pay attention to the mirror’s shape.

Definition
Spherical mirror

A mirror whose reflecting surface has the shape of a portion of a sphere. The curved surface may face inward or bulge outward.

Picture the curved wall of a hollow ball. A small part of that wall provides a useful model for a spherical mirror. The word spherical describes the surface shape; it does not mean that the mirror is a complete sphere. Also, a curved mirror is not automatically spherical: here we focus on the common spherical type.

Explore the two sides of a spoon

A shiny metal spoon gives us an easy way to compare two curved reflecting surfaces. Its bowl has an inner side that curves inward and an outer side that bulges outward. Although a spoon is not a perfect spherical mirror, it is useful for beginning this investigation.

Investigation — two sides of a spoon

Investigate whether surface shape and viewing distance affect your image. Use a clean, shiny metal spoon in ordinary room light. Compare the inner and outer surfaces with a flat mirror.

  1. Hold the inner surface near your face and observe whether your image is upright or upside down, larger or smaller.
  2. Slowly move the spoon farther away. Describe any change instead of assuming that the first appearance will remain.
  3. Turn the spoon around and repeat with the outer surface.
  4. Record the surface used, its distance, the image orientation, and its approximate size.

At some viewing distances the inner surface shows an inverted image: the top of the object appears at the bottom. Very close to the inward-curving surface, an upright enlarged image may be seen instead. The outer surface normally gives an upright smaller image. These observations suggest that inward and outward curves behave differently; the next lesson will investigate their image patterns more carefully.

Do not turn one observation into an always-rule

If the inner spoon surface shows an upside-down face at one distance, that does not mean an inward-curving mirror always gives an upside-down image. Distance matters. A spoon also has an irregular shape, so its images may be distorted.

Example — Read an observation

Problem
Riya sees a small upright image on one side of a spoon and an upside-down image on the other. What should she record?

  1. 1.First identify the actual surfaces: the small upright image is normally seen on the outward-bulging side.
  2. 2.Record the image on the inward-curving side as inverted at the distance she used.
  3. 3.Repeat at other distances before describing how the image changes. One result alone cannot establish every possible image.

Concave and convex reflecting surfaces

The names of spherical mirrors describe the surface that reflects the light. Look at this surface from the side, rather than judging the whole circular outline from above. Both types may look like round discs when viewed straight on, even though their curves are opposite.

Definition
Concave mirror

A spherical mirror whose reflecting surface curves inward, like the inside of a bowl.

Definition
Convex mirror

A spherical mirror whose reflecting surface bulges outward, like the outside of a bowl.

Concave mirrorConvex mirrorLight reachesthe hollow sideLight reachesthe bulging sideCurves inwardCurves outward
Identify the reflecting curve— The blue arrows point to the reflecting faces. Both mirrors are shown facing the viewer on the left of each panel.
Investigation — identify the curve

Place a concave mirror and a convex mirror with their reflecting surfaces facing upward. Bring your eye to the level of the mirrors and view them from the side. Decide whether the reflecting surface forms a hollow or a bulge. Handle the glass gently and compare what you see with the mirror definitions.

A schematic representation is a simplified drawing used to show the important features. In a mirror diagram, a curved line represents the surface and short shading strokes indicate the non-reflecting side. The unshaded side is the face from which light is reflected. The shading is therefore a clue, not decoration.

ConcaveConvexUnshaded face reflectsUnshaded face reflects
Read the shaded side— In these side-view sketches, light approaches from the left. The short strokes show the back of each mirror.
Example — Identify a mirror from the side

Problem
Two round mirrors have the same diameter. One has a reflecting hollow; the other has a reflecting bulge. How would you name them?

  1. 1.Their round outlines alone do not identify the type because both can have a circular outline.
  2. 2.The reflecting hollow curves inward, so that mirror is concave.
  3. 3.The reflecting bulge curves outward, so that mirror is convex.

A model of the shape, not a manufacturing method

Thinking of a piece of a hollow sphere helps you understand the geometry. It does not mean that manufacturers cut mirrors out of hollow glass balls. The source describes preparing a curved glass surface by grinding and polishing glass, then applying a reflective layer, such as aluminium.

Shape modelPart of a hollow sphereConcaveReflect from hollow sideConvexReflect from bulging sideOrange curve: coated glass boundary; blue arrow: incident light
Hollow-sphere model and coated faces— The highlighted arc models a curved glass piece. In the coated-glass model, distinguish the coating from the face used for reflection.

In the source’s coated-glass model, a coating on the outside of the curved glass allows the inner face to act as a concave mirror. Coating the inner curved side allows the outer face to act as a convex mirror. Keep the coated side and the reflecting face clear in your mind: classification follows the shape of the face from which light is reflected.

Example — Shape and coating

Problem
A diagram shows a small piece taken from an imaginary hollow sphere. Does this prove that a real mirror was made by cutting up a sphere?

  1. 1.No. The hollow sphere is a model that explains the shape of the surface.
  2. 2.A real curved glass piece can be prepared by shaping and polishing glass.
  3. 3.A reflective coating then makes it function as a mirror. The face used for reflection determines whether it is concave or convex.

Check your understanding

Use the reflecting surface, rather than the name of an object or its outline, to identify a mirror. The following questions also check whether you can distinguish a shape model from a real manufacturing process.

Quiz

Quick check

What makes a mirror a spherical mirror?

Quick check

A mirror’s reflecting face curves inward. It is a:

Quick check

Which spoon surface provides a simple model of a convex mirror?

Quick check

What do short shading strokes normally indicate in a mirror drawing?

Quick check

Why should you change the viewing distance in the spoon investigation?

Quick check

Which statement about the hollow-sphere model is correct?

Practice Problems

Practice Problems
  1. Define a spherical mirror in your own words and explain why a circular frame is not enough to identify one.
  2. Sketch side views of concave and convex mirrors. Indicate the reflecting face and shade the back.
  3. Describe the spoon investigation, including what you would record and which variable you would change.
  4. Explain why “the inner spoon always shows an inverted face” is an unsafe conclusion from one observation.
  5. Two mirrors look identical from above. Suggest a way of distinguishing them without relying on image size.
  6. Explain the difference between modelling a mirror as a piece of a hollow sphere and manufacturing a real mirror.

Key Takeaways

Key Takeaways

• A plane mirror is flat; a spherical mirror has a reflecting surface shaped like part of a sphere. • Concave describes an inward-curving reflecting face; convex describes an outward-bulging reflecting face. • The inner and outer sides of a shiny spoon help compare two kinds of curved reflection. • The appearance in an inward-curving surface can change with viewing distance. • Shading in a mirror sketch indicates the non-reflecting side. • The imaginary hollow sphere is a shape model; real mirrors are shaped, polished, and coated.