Ray diagram of a concave lens: all 2 cases
A concave lens always forms a virtual, erect and diminished image on the same side as the object, between the focus F₁ and the optical centre O.
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
2 positions of the object
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.
Object between infinity and O, f = 10 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
Quick answers
Can a concave lens form a real image?
No, not of a real object. The refracted rays always spread out, so they only appear to come from a point on the object side.
Where is a concave lens used?
In spectacles for short sight (myopia), and in door peepholes and some telescopes.
Where is the image of a far object?
At the focus F₁ on the object side, highly diminished and point-sized.