Spherical mirrors: concave and convex
The inside of a steel spoon shows your face upside down, while its back shows a small upright face. At a fun fair, curved mirrors make you look tall, wide or tiny.
A spherical mirror is a mirror whose reflecting surface is a part of a hollow sphere. If the reflecting surface curves inwards it is a concave mirror; if it curves outwards it is a convex mirror.
Key idea 1: Two kinds of curved mirror — A concave mirror is hollow like the inside of a bowl. A convex mirror bulges like the back of a bowl. In diagrams the back, non-reflecting side is shaded. To tell them apart, place the mirror on a table with the reflecting side up and look from the side at eye level.
- Easy: A mirror that curves inwards is concave; one that curves outwards is convex.
- Medium: A torch reflector curves inwards, so it is a concave mirror.
- Exam-type: Viewed from the side, a mirror whose reflecting surface is hollow at the middle is concave, and one that bulges towards you is convex.
In the figure: The concave mirror is hollow towards the light, the convex mirror bulges towards it, and the plane mirror is flat.
Key idea 2: A spoon is a mirror too — The inner side of a shiny steel spoon behaves like a concave mirror and the outer side like a convex mirror. A spherical mirror is made by grinding and polishing flat glass into a curve, not by slicing a hollow glass ball. Silvering the outer curved surface gives a concave mirror, and silvering the inner curved surface gives a convex mirror.
- Easy: The back of a spoon shows an erect, smaller image of your face.
- Medium: A coating of aluminium on the outer curved surface of curved glass makes a concave mirror.
- Exam-type: The same spoon shows a different image on each side because one side acts as a concave mirror and the other as a convex mirror.
In the figure: Turning the spoon over changes the type of mirror and so changes the image.
Concave curves inwards and convex curves outwards, and a plane mirror is flat.
Thinking a spherical mirror is cut from a hollow glass ball. It is made by grinding and polishing flat glass.
Concave has a cave, a hollow, in it. Memory clue: Concave = Cave; Convex = bulging out.
Spot the difference
| Feature | Concave mirror | Convex mirror |
|---|---|---|
| reflecting surface | curves inwards | curves outwards |
| inside of a spoon | yes | no |
| example | torch reflector | side-view mirror |
Practice questions
- 1What is a spherical mirror?
- 2Which mirror curves inwards?
- 3Which side of a steel spoon acts like a convex mirror?
- 4How is the non-reflecting back of a mirror shown in a diagram?
- 5How can you tell a concave mirror from a convex one using the side view?
- 6How is a spherical mirror made?
- 7A coating is put on the inner curved surface of a curved glass piece. Which mirror does it become?
- 8A girl sees a very big face in one curved mirror and a tiny face in another. What does this show?
Show answers (try them yourself first)
- 1A mirror whose reflecting surface is a part of a hollow sphere.
- 2The concave mirror.
- 3The outer, bulging side.
- 4It is shaded.
- 5Keep the eye at table level; if the reflecting surface is hollow at the middle it is concave, and if it bulges towards you it is convex.
- 6By grinding and polishing a flat piece of glass into a curve.
- 7A convex mirror, because the coated surface then bulges outwards.
- 8That different curved mirrors form different kinds of images.
Images formed by spherical mirrors and their uses
A dentist holds a small mirror close to a tooth and sees it big. A motorbike rider glances at the side mirror and sees the whole road behind in a small picture.
A concave mirror can form enlarged, same-size or diminished images, erect or inverted, depending on how far the object is. A convex mirror always forms an erect and diminished image.
Key idea 1: How the images change — With the object very close, a concave mirror gives an erect and enlarged image. As the object moves farther, the image turns inverted, is first big and then keeps getting smaller. A convex mirror always gives an erect, smaller image, and it shrinks only a little as the object moves away. A plane mirror gives an erect image of the same size. Lateral inversion is seen in all three mirrors.
- Easy: A convex mirror always gives an erect and smaller image.
- Medium: A concave mirror gives an enlarged, erect image of an object kept very close to it.
- Exam-type: A mirror that gives an erect, smaller image at every distance must be convex.
In the figure: The same concave mirror shows a small upside-down image from afar and a big upright one from close by.
Key idea 2: Uses of the mirrors — Torch reflectors, car headlights and a dentist's mirror are concave. The main mirror of most modern telescopes is a large concave mirror. Side-view mirrors of vehicles, road-bend safety mirrors and shop security mirrors are convex, because they give an erect image and a wide view. A side-view mirror warns that objects are closer than they appear, because its smaller images make them look farther.
- Easy: Side-view mirrors of vehicles are convex.
- Medium: A dentist uses a concave mirror because it gives an enlarged view of a tooth held close.
- Exam-type: A convex mirror at a sharp bend lets drivers on both sides see each other's traffic, as it shows a wide area.
In the figure: Concave mirrors are used for light and a close enlarged look; convex mirrors are used for a wide view.
Concave mirror: size and direction change with distance. Convex mirror: always erect and smaller.
Thinking that a convex mirror enlarges objects. It makes them smaller but shows a wider area.
Wide view means convex; close, enlarged look means concave. Memory clue: Convex = Covers a lot; Concave = Close-up.
Spot the difference
| Feature | Concave mirror | Convex mirror |
|---|---|---|
| image | enlarged or smaller, erect or inverted | always erect and smaller |
| view area | narrow | wide |
| use | torch, dentist | side-view mirror |
Practice questions
- 1Which mirror always forms an erect and smaller image?
- 2Name one use of a concave mirror.
- 3Name one use of a convex mirror.
- 4Why does a dentist use a concave mirror?
- 5Why are convex mirrors used as side-view mirrors?
- 6What happens to the image in a concave mirror when the object moves far away?
- 7Why does a side-view mirror say "Objects in mirror are closer than they appear"?
- 8A girl walks towards a large concave mirror from far away. Describe the image she sees.
Show answers (try them yourself first)
- 1The convex mirror.
- 2Torch reflector (also headlight, dentist mirror, telescope mirror).
- 3Side-view mirror (also road-bend mirror, shop mirror).
- 4Held close to a tooth, it gives an enlarged view.
- 5They give an erect image and a wide view of the traffic behind.
- 6The image becomes inverted and gets smaller.
- 7A convex mirror makes images smaller, so objects look farther than they really are.
- 8First a small inverted image that grows larger; when she is very close, it becomes erect and magnified.
Laws of reflection
A ball thrown at a wall at a slant bounces away at a matching slant. A torch beam aimed at a bathroom mirror lands on the opposite wall at a predictable spot.
The ray that falls on a mirror is the incident ray and the ray that comes back is the reflected ray. The normal is a line at 90° to the mirror at the point where the ray falls.
Key idea 1: Angles of incidence and reflection — The angle of incidence (i) is between the normal and the incident ray; the angle of reflection (r) is between the normal and the reflected ray. First law: the angle of incidence is equal to the angle of reflection. Both angles are measured from the normal, not from the mirror. A ray along the normal has i = 0° and r = 0°, and returns along the same path.
- Easy: If i is 35°, then r is also 35°.
- Medium: If i is 25°, the reflected ray makes 90° − 25° = 65° with the mirror surface.
- Exam-type: A ray making 30° with the mirror surface has i = 90° − 30° = 60°, so r = 60°, and the angle between the incident and reflected rays is 120°.
In the figure: The two angles on either side of the normal are equal.
Laws of reflection
In the app you can move this figure with your finger.
Open in the appKey idea 2: Same plane, and every mirror — Second law: the incident ray, the normal and the reflected ray all lie in the same plane. In the chart-paper activity, the reflected beam vanished when the paper was bent and returned when it was flattened. Both laws hold for plane, concave and convex mirrors. A curved mirror still obeys them at every point, but its normal points in a different direction at each point, so parallel rays do not stay parallel.
- Easy: The incident ray, the normal and the reflected ray lie in one plane.
- Medium: Two rays hitting the same point at different angles have the same normal.
- Exam-type: Parallel rays spread or gather after a curved mirror because the normal differs from point to point, though each ray obeys the laws.
In the figure: One law is about the size of the angles, the other about the plane.
Angles are measured from the normal, and the laws hold for all mirrors.
Measuring the angle of incidence from the mirror surface. It is measured from the normal.
Find i first, then r equals i. Memory clue: i = r, Ray comes Right back at the same angle.
Spot the difference
| Feature | Angle of incidence | Angle of reflection |
|---|---|---|
| between | normal and incident ray | normal and reflected ray |
| symbol | i | r |
| size | equal to r | equal to i |
Practice questions
- 1What is the normal?
- 2State the first law of reflection.
- 3What are i and r when a ray falls along the normal?
- 4The angle of incidence is 40°. Find the angle of reflection.
- 5A ray makes 30° with the mirror surface. Find the angle of reflection.
- 6What does the chart-paper activity prove?
- 7The angle of incidence is 30°. Find the angle between the incident ray and the reflected ray.
- 8Why do parallel rays not stay parallel after a curved mirror, though each obeys the laws?
Show answers (try them yourself first)
- 1A line drawn at 90° to the mirror at the point of incidence.
- 2The angle of incidence is equal to the angle of reflection.
- 3Both are 0°, and the ray returns along the same path.
- 440°.
- 5The angle with the normal is 90° − 30° = 60°, so r = 60°.
- 6That the incident ray, the normal and the reflected ray lie in the same plane.
- 730° + 30° = 60°.
- 8The normal points in a different direction at each point of the curved surface, so each ray turns differently.
Converging and diverging of light by mirrors
A magnifying mirror in sunlight can make a bright dot hot enough to smoke a paper. A shop's round mirror at the corner spreads your view across the whole shop.
Rays converge when they come closer together and diverge when they spread apart. A concave mirror converges parallel rays and a convex mirror diverges them, while a plane mirror keeps them parallel.
Key idea 1: Three mirrors, three results — Parallel beams reflected by a plane mirror stay parallel. A concave mirror brings them together, so it is also called a converging mirror. A convex mirror spreads them apart, so it is a diverging mirror. Each ray obeys the laws of reflection; the shape of the surface does the rest.
- Easy: A concave mirror makes parallel rays come closer together.
- Medium: If reflected beams spread out, the mirror is convex.
- Exam-type: X keeps parallel beams parallel, Y brings them together and Z spreads them; X is plane, Y is concave and Z is convex.
In the figure: The plane mirror keeps rays parallel, the concave mirror gathers them and the convex mirror spreads them.
Key idea 2: Burning paper and solar concentrators — A concave mirror held towards the Sun gathers the reflected light into a small bright spot that is hot enough to burn paper. A convex or plane mirror cannot do this. Devices that gather sunlight into a small area are solar concentrators. They heat a liquid to make steam for electricity, or give heat for large-scale cooking and for solar furnaces, which can even melt steel. Never look at the Sun or its reflection; aim the light only at paper.
- Easy: A solar cooker uses mirrors that converge sunlight to give heat.
- Medium: A sharp, small bright spot appears only when the paper is at the right distance from the mirror.
- Exam-type: A convex mirror cannot burn paper because it spreads the light instead of concentrating it.
In the figure: Sunlight gathered at a spot makes heat; the eyes must never be in the way.
Concave converges, convex diverges, plane keeps parallel.
Thinking a mirror makes its own heat. The heat comes from the Sun's light gathered in one spot.
Concave = Collects light. Memory clue: Concave Collects, Convex Spreads.
Spot the difference
| Feature | Concave mirror | Convex mirror |
|---|---|---|
| parallel beam after reflection | comes together | spreads apart |
| can burn paper | yes | no |
| also called | converging mirror | diverging mirror |
Practice questions
- 1What do the words converge and diverge mean?
- 2Which mirror makes parallel rays converge?
- 3Which mirror keeps parallel rays parallel?
- 4Why does a bright spot on paper burn it?
- 5What safety rule must be followed with the Sun and a mirror?
- 6What is a solar concentrator?
- 7Why can a convex mirror not burn paper?
- 8Parallel beams fall on mirrors X, Y and Z. X keeps them parallel, Y gathers them and Z spreads them. Name X, Y and Z.
Show answers (try them yourself first)
- 1Converge: come closer together; diverge: spread apart.
- 2The concave mirror.
- 3The plane mirror.
- 4The light gets concentrated there and makes enough heat.
- 5Never look at the Sun or its reflection; focus the light only on paper.
- 6A device that gathers sunlight into a small area, using mirrors or lenses.
- 7It spreads the light out instead of gathering it at one spot.
- 8X is plane, Y is concave and Z is convex.
Lenses: convex and concave
A magnifying glass makes small print big. A spectacle lens, a phone camera lens and the lens inside your own eye all bend light.
A lens is a piece of transparent material, like glass or plastic, with curved surfaces. A convex lens is thicker at the middle and a concave lens is thicker at the edges. We see things through a lens, not in it.
Key idea 1: Images through lenses — An object close behind a convex lens looks erect and enlarged; farther away it looks inverted, first big and then smaller. A concave lens always shows an erect, smaller image. A round water drop on glass acts like a small convex lens and makes the letters below look bigger. A magnifying glass is a convex lens.
- Easy: A magnifying glass is a convex lens.
- Medium: A concave lens always shows an erect and smaller image.
- Exam-type: A lens that shows an object inverted from afar and erect and enlarged from near is a convex lens.
In the figure: The convex lens bulges in the middle; the concave lens is thin in the middle.
Lenses: convex and concave
In the app you can move this figure with your finger.
Open in the appKey idea 2: Converging and diverging lenses — A thin flat glass plate lets a parallel beam pass unchanged. A convex lens converges it, so it is a converging lens and can burn paper in sunlight. A concave lens diverges it, so it is a diverging lens and cannot. Lenses are used in spectacles, cameras, telescopes and microscopes, and the eye has a convex lens that can change its shape.
- Easy: A convex lens is also called a converging lens.
- Medium: A concave lens cannot burn paper because it spreads the light.
- Exam-type: A convex lens burns paper by converging sunlight, but never look at the Sun through it.
In the figure: The flat plate keeps the beam straight, the convex lens gathers it and the concave lens spreads it.
Convex lens converges and concave lens diverges; mirrors reflect while lenses let light pass.
Mixing up mirrors and lenses. We look into a mirror but through a lens.
Thick middle = convex = converges. Memory clue: Convex Collects, Concave Cuts it wide.
Spot the difference
| Feature | Convex lens | Concave lens |
|---|---|---|
| thicker part | middle | edges |
| parallel beam | converges | diverges |
| image | depends on distance | always erect and smaller |
Practice questions
- 1What is a lens?
- 2Which lens is thicker at the middle?
- 3What other name does a concave lens have?
- 4Why does a water drop make letters look bigger?
- 5Why can a convex lens burn paper but a concave lens cannot?
- 6Name two devices that use lenses.
- 7Through a lens, an object looks inverted from far and erect and enlarged from near. Which lens is it?
- 8How is a lens different from a mirror in the way we see things?
Show answers (try them yourself first)
- 1A piece of transparent material with curved surfaces.
- 2The convex lens.
- 3Diverging lens.
- 4Its outward-curved surface acts like a convex lens.
- 5The convex lens converges sunlight to a spot, but the concave lens spreads it.
- 6For example spectacles and cameras (also telescopes, microscopes).
- 7A convex lens.
- 8We see things through a lens because light passes through it, but in a mirror because light bounces back.