Numford
Ray diagrams

Ray diagram of a convex mirror: all 2 cases

A convex mirror always forms a virtual, erect and diminished image behind the mirror, between the pole P and the focus F.

The ray diagram

Drag the object or type values. Signs follow the New Cartesian convention: distances are measured from the pole or optical centre, along the incident light is positive, against it negative, and heights above the axis are positive. So u is negative for a real object.

Image distance v+6.67 cmbehind the mirror
Magnification m+0.33erect, 0.33 times
Image height h′+0.67 cmobject +2 cm
Focal length f+10 cmR = 2f = +20 cm
NatureVirtual, erect, diminishedObject between infinity and the pole P
Image positionBetween P and F, behind the mirrorDiminished

Convex mirror of focal length +10 cm. An object +2 cm tall at u = -20 cm: the image is at v = +6.67 cm, virtual, erect, diminished.

Unit
cm
Show the working
  1. f = R/2 = +20/2 = +10 cm, u = -20 cm (the object is in front, so u is negative), h = +2 cm.
  2. 1/v = 1/f - 1/u = 1/(+10) - 1/(-20) = 30/200 = 3/20
  3. v = +6.67 cm: positive, so the image is behind the mirror and virtual.
  4. m = -v/u = -(+6.67)/(-20) = +0.33: positive, so erect, and diminished.
  5. h′ = m × h = +0.33 × +2 = +0.67 cm
All the cases

2 positions of the object

NCERT table

Image formation by a convex mirror

ObjectImageSizeNature
At infinityAt the focus F, behind the mirrorHighly diminished, point-sizedVirtual and erect
Between infinity and the pole PBetween P and F, behind the mirrorDiminishedVirtual and erect
How to draw it

The rays to use

  • A ray parallel to the principal axis reflects as if it came from the focus F behind the mirror.
  • A ray heading towards the centre of curvature C reflects back along the same path.
  • A ray heading towards the focus F reflects parallel to the principal axis.
  • The reflected rays spread out, so the image is where their extensions meet behind the mirror.
With numbers

Object between infinity and the pole, f = 10 cm

  1. f = R/2 = +20/2 = +10 cm, u = -20 cm (the object is in front, so u is negative), h = +2 cm.
  2. 1/v = 1/f - 1/u = 1/(+10) - 1/(-20) = 30/200 = 3/20
  3. v = +6.67 cm: positive, so the image is behind the mirror and virtual.
  4. m = -v/u = -(+6.67)/(-20) = +0.33: positive, so erect, and diminished.
  5. h′ = m × h = +0.33 × +2 = +0.67 cm
Questions

Quick answers

Can a convex mirror form a real image?

No, not of a real object. The reflected rays always spread out, so they only appear to meet behind the mirror.

Why are convex mirrors used as rear-view mirrors?

They always give an erect image, and because the image is smaller they show a much wider area behind the vehicle.

Where is the image when the object is far away?

At the focus F behind the mirror, highly diminished and point-sized.

Try your own mirror or lens