Numford
Ray diagram

Ray diagram of a convex lens when the object is between F₁ and O

The image is on the same side of the lens as the object: virtual and erect, enlarged.

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 cmon the object side
Magnification m+2erect, 2 times
Image height h′+4 cmobject +2 cm
Power P+10 Dconverging
NatureVirtual, erect, enlargedObject between F₁ and the optical centre O
Image positionOn the same side of the lens as the objectEnlarged

Convex lens of focal length +10 cm. An object +2 cm tall at u = -5 cm: the image is at v = -10 cm, virtual, erect, enlarged.

Unit
cm
Show the working
  1. f = +10 cm, u = -5 cm (the object is in front, so u is negative), h = +2 cm.
  2. 1/v = 1/f + 1/u = 1/(+10) + 1/(-5) = -5/50 = -1/10
  3. v = -10 cm: negative, so the image is on the object side and virtual.
  4. m = v/u = (-10)/(-5) = +2: positive, so erect, and enlarged.
  5. h′ = m × h = +2 × +2 = +4 cm
  6. Power P = 1/f = 1/(+0.1 m) = +10 D
With numbers

Take f = 10 cm and the object at 5 cm

  1. f = +10 cm, u = -5 cm (the object is in front, so u is negative), h = +2 cm.
  2. 1/v = 1/f + 1/u = 1/(+10) + 1/(-5) = -5/50 = -1/10
  3. v = -10 cm: negative, so the image is on the object side and virtual.
  4. m = v/u = (-10)/(-5) = +2: positive, so erect, and enlarged.
  5. h′ = m × h = +2 × +2 = +4 cm
  6. Power P = 1/f = 1/(+0.1 m) = +10 D
NCERT table

Image formation by a convex lens

ObjectImageSizeNature
At infinityAt the focus F₂Highly diminished, point-sizedReal and inverted
Beyond 2F₁Between F₂ and 2F₂DiminishedReal and inverted
At 2F₁At 2F₂Same sizeReal and inverted
Between F₁ and 2F₁Beyond 2F₂EnlargedReal and inverted
At the focus F₁At infinityInfinitely large or highly enlargedReal and inverted
Between F₁ and the optical centre OOn the same side of the lens as the objectEnlargedVirtual and erect
How to draw it

The rays to use

  • A ray parallel to the principal axis passes through the focus F₂ on the other side after refraction.
  • A ray through the optical centre O goes straight on without bending.
  • A ray through the focus F₁ comes out parallel to the principal axis.
  • Where the refracted rays meet is the top of the image.
Where it is used

In real life

  • A magnifying glass, the simple microscope: an enlarged, erect, virtual image.
Questions

Quick answers

Where is the image when the object is between F₁ and O of a convex lens?

The image is on the same side of the lens as the object: virtual and erect, enlarged. With f = 10 cm and the object at 5 cm, v = -10 cm and m = +2.

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?

A magnifying glass, the simple microscope: an enlarged, erect, virtual image.

Try your own mirror or lens