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Lesson 3 of 10Light & Geometric Optics
Unit 4 · Lesson 3 of 10

Concave and Convex Mirrors with Ray Diagrams

The parts of a curved mirror, the principal rays that make ray diagrams quick, how the image in a concave mirror changes as the object moves, and why convex mirrors always give small, upright, virtual images.

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Key things to remember

  1. 1Concave mirrors converge parallel rays to F; convex mirrors diverge them as if from a virtual F behind the mirror.
  2. 2Focal length is half the radius of curvature: .
  3. 3Concave rays: parallel → through F; through F → parallel; through C → back on itself.
  4. 4Concave mirror: object beyond C gives a smaller, inverted, real image between C and F; object inside F gives a larger, upright, virtual image behind the mirror; object at F gives no image.
  5. 5Convex mirror: always smaller, upright, virtual, behind the mirror between V and F.

A spoon is two mirrors in one. Look into the bowl and your face is upside down; flip it over and your face is upright but tiny. Curved mirrors are everywhere once you notice them: the shiny bowl behind a car headlight, the domed mirror in the corner of a store, the magnifying mirror used for putting in contact lenses, and the giant dish of a research telescope. All of them follow the law of reflection at every point. The curve just tilts the normal from point to point, which makes the reflected rays spread out or come together.

Parts of a curved mirror

  • Concave mirror: the reflecting surface curves inward like a cave (the inside of a spoon). It is a converging mirror: parallel rays reflect toward one point.
  • Convex mirror: the reflecting surface bulges outward (the back of a spoon). It is a diverging mirror: parallel rays reflect and spread apart.
  • Vertex (V): the centre point of the mirror's surface.
  • Principal axis: the line through the vertex perpendicular to the mirror.
  • Centre of curvature (C): the centre of the sphere the mirror is cut from. The distance from C to V is the radius of curvature .
  • Focal point (F): where rays parallel to the principal axis meet after reflecting (concave), or appear to come from (convex). It sits halfway between C and V.
  • Focal length (): the distance from F to V, so .
The principal rays for a concave mirror
Ray 1 travels parallel to the principal axis and reflects through F. Ray 2 travels through F and reflects parallel to the principal axis. Ray 3 travels through C, hits the mirror head-on along a normal, and reflects straight back on itself. Any two of these locate the image; the third is a check.
principal axisconcave mirrorFCobjectreal image1 parallel to the axis → reflects through F2 through F → reflects parallel to the axis3 through C → reflects straight back on itselfC = centre of curvature (2f from the mirror); image: real, inverted, smaller
Fig 1A concave mirror with the principal axis, F and C marked (C is twice as far from the mirror as F). The object stands beyond C, and the three principal rays meet between F and C to form a real, inverted, smaller image.

The rays are reversible, which is why rules 1 and 2 are mirror images of each other: a ray coming in parallel goes out through F, so a ray coming in through F goes out parallel. A ray through C strikes the mirror along a radius, and a radius is always perpendicular to a circle, so that ray is along the normal and its angle of incidence is .

Object position (concave mirror)SizeAttitudeLocationTypeUse
Beyond CSmallerInvertedBetween C and FRealReflecting telescope (distant objects)
At CSame sizeInvertedAt CRealFinding C in the lab: the image lands on the object
Between C and FLargerInvertedBeyond CRealProjector-style reflectors
At FNo clear image——Reflected rays leave parallelFlashlight and headlight reflector (bulb at F)
Between F and VLargerUprightBehind the mirrorVirtualMakeup, shaving and dental mirrors
As the object moves in from far away toward F, the real image moves out from F and grows. Inside F the image jumps behind the mirror and becomes virtual.
Headlights and solar cookers run the rule both ways
Put a bulb at F and the reflected rays leave parallel, making a strong, straight beam. Point the same mirror at the Sun, whose rays arrive parallel, and they all meet at F, which is why a concave solar cooker or a satellite dish puts its pot or receiver at the focal point.

Convex mirrors

For a convex mirror, F and C are behind the mirror, so they are virtual points. The principal rays are adjusted: Ray 1 travels parallel to the principal axis and reflects as if it came from F (draw the dashed extension back through F). Ray 2 is aimed at F behind the mirror and reflects parallel to the principal axis. Ray 3 is aimed at C and reflects straight back on itself. The reflected rays always spread apart, so they never meet in front of the mirror; only their dashed extensions meet, behind it.

principal axisconvex mirrorFCobjectvirtual image1 parallel to the axis → reflects as if from F2 toward F → reflects parallel to the axis3 toward C → reflects straight backDashed lines: extensions behind the mirror. Image: virtual, upright, smaller.
Fig 2A convex mirror with a virtual focal point behind it. Reflected rays diverge, and their dashed extensions meet behind the mirror, between the mirror and F, at an upright, smaller, virtual image.
AConcave (converging)
  • Image depends on where the object is
  • Real and inverted when the object is outside F
  • Virtual, upright and larger when the object is inside F
  • Uses: headlights, telescopes, makeup mirrors, solar cookers
BConvex (diverging)
  • Same type of image wherever the object is
  • Always smaller, upright and virtual, between V and F behind the mirror
  • Shows a wide field of view
  • Uses: store security mirrors, passenger-side car mirrors, blind-corner mirrors
Objects in mirror are closer than they appear
That warning is printed on passenger-side car mirrors because they are convex. The wide view is great for spotting cars in the next lane, but the shrunken image makes cars look farther away than they really are.
Loading interactive…
Choose a concave or convex mirror and drag the object along the axis: watch the principal rays, the image's size, attitude, location and type, and the mirror equation worked out for each position.

Worked examples

Reveal one step at a time and try to beat it to the next line.

Example 1
An object stands between C and F in front of a concave mirror. Use the principal rays to describe the image (SALT).
Example 2
A concave mirror has a radius of curvature of . Where should a bulb be placed to make a parallel beam, and what kind of image would a face from the mirror see?
Example 3
Explain why stores use convex mirrors, not concave ones, to watch the aisles.

Where marks get lost

  • Drawing the ray through F for a concave mirror reflecting through F again. A ray that arrives through F leaves parallel to the axis; a ray that arrives parallel leaves through F.
  • Placing C at the focal point. C is twice as far from the mirror as F: .
  • Expecting a convex mirror to give an inverted or enlarged image for some object positions. Its image is always smaller, upright and virtual.
  • Forgetting dashed lines for extensions behind a mirror. Light never travels behind a mirror, so anything drawn there must be dashed and the image there is virtual.
  • Saying an object at F forms an image 'at infinity' and then describing its SALT. At F the reflected rays are parallel and no image forms.

Flashcards 8

Concave mirror
Convex mirror
Focal length and radius of curvature
Concave principal rays
+ 4 more

Practice

1
A concave mirror has a radius of curvature of . What is its focal length, in cm?
cm
2
A ray travelling parallel to the principal axis strikes a concave mirror. Where does it go after reflecting?
3
Match each object position in front of a concave mirror to the image it produces.
Beyond C
At C
Between C and F
Between F and the mirror
4
Which is true of every image formed by a convex mirror?
5
Where, relative to a concave reflector, should the bulb in a flashlight be placed to produce a parallel beam? (Name the point.)
6
Why do passenger-side car mirrors carry the warning 'objects in mirror are closer than they appear'?
7
An object is placed exactly at C in front of a concave mirror with . Where is the image?
8
An object starts far from a concave mirror and moves steadily toward F. Sort the real image's size, from first to last.
  1. 1Same size as the object
  2. 2Very large and very far away
  3. 3Larger than the object
  4. 4Much smaller than the object

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