Ray diagram of a convex lens when the object is beyond 2F₁
The image is between F₂ and 2F₂: real and inverted, 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.
Convex lens of focal length +10 cm. An object +2 cm tall at u = -30 cm: the image is at v = +15 cm, real, inverted, diminished.
Show the working
- f = +10 cm, u = -30 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f + 1/u = 1/(+10) + 1/(-30) = 20/300 = 1/15
- v = +15 cm: positive, so the image is behind the lens and real.
- m = v/u = (+15)/(-30) = -0.5: negative, so inverted, and diminished.
- h′ = m × h = -0.5 × +2 = -1 cm
- Power P = 1/f = 1/(+0.1 m) = +10 D
Take f = 10 cm and the object at 30 cm
- f = +10 cm, u = -30 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f + 1/u = 1/(+10) + 1/(-30) = 20/300 = 1/15
- v = +15 cm: positive, so the image is behind the lens and real.
- m = v/u = (+15)/(-30) = -0.5: negative, so inverted, and diminished.
- h′ = m × h = -0.5 × +2 = -1 cm
- Power P = 1/f = 1/(+0.1 m) = +10 D
Image formation by a convex lens
| Object | Image | Size | Nature |
|---|---|---|---|
| At infinity | At the focus F₂ | Highly diminished, point-sized | Real and inverted |
| Beyond 2F₁ | Between F₂ and 2F₂ | Diminished | Real and inverted |
| At 2F₁ | At 2F₂ | Same size | Real and inverted |
| Between F₁ and 2F₁ | Beyond 2F₂ | Enlarged | Real and inverted |
| At the focus F₁ | At infinity | Infinitely large or highly enlarged | Real and inverted |
| Between F₁ and the optical centre O | On the same side of the lens as the object | Enlarged | Virtual and erect |
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.
In real life
- A camera: a far object gives a small, real, inverted image on the sensor or film.
Quick answers
Where is the image when the object is beyond 2F₁ of a convex lens?
The image is between F₂ and 2F₂: real and inverted, diminished. With f = 10 cm and the object at 30 cm, v = +15 cm and m = -0.5.
Is this image real or virtual?
Real: the rays actually meet there, so the image can be caught on a screen. Real images formed by one mirror or lens are inverted.
Where is this used?
A camera: a far object gives a small, real, inverted image on the sensor or film.