Numford
Ray diagram

Ray diagram of a convex mirror when the object is between infinity and the pole

The image is between P and F, behind the mirror: virtual and erect, diminished.

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
With numbers

Take f = 10 cm and the object at 20 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
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.
Where it is used

In real life

  • Rear-view mirrors of vehicles: always an erect, smaller image, and a much wider field of view than a plane mirror.
Questions

Quick answers

Where is the image when the object is between infinity and the pole of a convex mirror?

The image is between P and F, behind the mirror: virtual and erect, diminished. With f = 10 cm and the object at 20 cm, v = +6.67 cm and m = +0.33.

Is this image real or virtual?

Virtual: the rays only appear to meet when traced back, so no screen can catch it. Virtual images formed by one mirror or lens are erect.

Where is this used?

Rear-view mirrors of vehicles: always an erect, smaller image, and a much wider field of view than a plane mirror.

Try your own mirror or lens