Ray diagram of a convex lens: all 6 cases
A convex lens forms a real, inverted image for every object position except between F₁ and O, where the image is virtual, erect and 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.
Convex lens of focal length +10 cm. An object +2 cm tall at u = -15 cm: the image is at v = +30 cm, real, inverted, enlarged.
Show the working
- f = +10 cm, u = -15 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f + 1/u = 1/(+10) + 1/(-15) = 5/150 = 1/30
- v = +30 cm: positive, so the image is behind the lens and real.
- m = v/u = (+30)/(-15) = -2: negative, so inverted, and enlarged.
- h′ = m × h = -2 × +2 = -4 cm
- Power P = 1/f = 1/(+0.1 m) = +10 D
6 positions of the object
- Object at infinity At the focus F₂. Real and inverted, highly diminished, point-sized.
- Object beyond 2F₁ Between F₂ and 2F₂. Real and inverted, diminished.
- Object at 2F₁ At 2F₂. Real and inverted, same size.
- Object between F₁ and 2F₁ Beyond 2F₂. Real and inverted, enlarged.
- Object at the focus F₁ At infinity. Real and inverted, infinitely large or highly enlarged.
- Object between F₁ and the optical centre O On the same side of the lens as the object. Virtual and erect, enlarged.
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.
Object between 2F₁ and F₁, f = 10 cm
- f = +10 cm, u = -15 cm (the object is in front, so u is negative), h = +2 cm.
- 1/v = 1/f + 1/u = 1/(+10) + 1/(-15) = 5/150 = 1/30
- v = +30 cm: positive, so the image is behind the lens and real.
- m = v/u = (+30)/(-15) = -2: negative, so inverted, and enlarged.
- h′ = m × h = -2 × +2 = -4 cm
- Power P = 1/f = 1/(+0.1 m) = +10 D
Quick answers
How many cases of image formation are there for a convex lens?
Six: the object at infinity, beyond 2F₁, at 2F₁, between F₁ and 2F₁, at F₁, and between F₁ and the optical centre O.
When does a convex lens act as a magnifying glass?
When the object is between F₁ and O. The image is then virtual, erect and enlarged, on the same side as the object.
When is the image the same size as the object?
When the object is at 2F₁. The image forms at 2F₂ on the other side, real and inverted.