Numford
Ray diagram

Ray diagram of a convex mirror when the object is at infinity

The image is at the focus F, behind the mirror: virtual and erect, highly diminished, point-sized.

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+10 cmbehind the mirror
Magnification m0a point
Image height h′0 cmobject +2 cm
Focal length f+10 cmR = 2f = +20 cm
NatureVirtual, erect, highly diminishedObject at infinity
Image positionAt the focus F, behind the mirrorHighly diminished, point-sized

Convex mirror of focal length +10 cm. An object far away: the image is at v = +10 cm, virtual, erect, highly diminished.

Unit
cm
Show the working
  1. f = R/2 = +20/2 = +10 cm. The object is at infinity, so u = -∞ and 1/u = 0.
  2. 1/v + 1/u = 1/f gives 1/v = 1/f, so v = f = +10 cm.
  3. The rays meet as if at the focus: a point-sized image, virtual and erect.
With numbers

Take f = 10 cm

  1. f = R/2 = +20/2 = +10 cm. The object is at infinity, so u = -∞ and 1/u = 0.
  2. 1/v + 1/u = 1/f gives 1/v = 1/f, so v = f = +10 cm.
  3. The rays meet as if at the focus: a point-sized image, virtual and erect.
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: traffic far behind shows up as a tiny, erect image.
Questions

Quick answers

Where is the image when the object is at infinity of a convex mirror?

The image is at the focus F, behind the mirror: virtual and erect, highly diminished, point-sized. With f = 10 cm, v = +10 cm.

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: traffic far behind shows up as a tiny, erect image.

Try your own mirror or lens