Ray diagram of a concave lens when the object is between infinity and O
The image is between F₁ and O: 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.
Concave lens 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.
Show the working
- f = -10 cm, u = -20 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f + 1/u = 1/(-10) + 1/(-20) = -30/200 = -3/20
- v = -6.67 cm: negative, so the image is on the object side and virtual.
- m = v/u = (-6.67)/(-20) = +0.33: positive, so erect, and diminished.
- h′ = m × h = +0.33 × +2 = +0.67 cm
- Power P = 1/f = 1/(-0.1 m) = -10 D
Take f = 10 cm and the object at 20 cm
- f = -10 cm, u = -20 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f + 1/u = 1/(-10) + 1/(-20) = -30/200 = -3/20
- v = -6.67 cm: negative, so the image is on the object side and virtual.
- m = v/u = (-6.67)/(-20) = +0.33: positive, so erect, and diminished.
- h′ = m × h = +0.33 × +2 = +0.67 cm
- Power P = 1/f = 1/(-0.1 m) = -10 D
Image formation by a concave lens
| Object | Image | Size | Nature |
|---|---|---|---|
| At infinity | At the focus F₁ | Highly diminished, point-sized | Virtual and erect |
| Between infinity and the optical centre O | Between F₁ and O | Diminished | Virtual and erect |
The rays to use
- A ray parallel to the principal axis spreads out after refraction, as if it came from the focus F₁ on the object side.
- A ray through the optical centre O goes straight on without bending.
- A ray heading towards the focus F₂ on the far side comes out parallel to the principal axis.
- The rays spread out, so the image is where their extensions meet, on the object side.
In real life
- Door peepholes and spectacles for myopia: always an erect, smaller, virtual image.
Quick answers
Where is the image when the object is between infinity and O of a concave lens?
The image is between F₁ and O: 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?
Door peepholes and spectacles for myopia: always an erect, smaller, virtual image.