A lens refracts light to form an image. Converging (convex) lenses bring parallel rays of light to a focus at the focal point and can form both real and virtual images. Diverging (concave) lenses spread rays outward, always forming virtual images. The power of a lens in dioptres is the reciprocal of its focal length in metres.
What are the two types of lens?
| Feature | Converging (convex) lens | Diverging (concave) lens |
|---|---|---|
| Shape | Thicker in the centre | Thinner in the centre |
| Effect on parallel rays | Bends toward the principal axis; converges at the focal point | Bends away from the principal axis; rays appear to diverge from the focal point |
| Focal point | Real — rays actually pass through it | Virtual — rays only appear to come from it |
| Power | Positive (+) | Negative (−) |
| Use | Camera, projector, magnifying glass, corrective lens for long-sightedness | Corrective lens for short-sightedness |
What is the focal length and how is it defined?
The focal length (f) of a lens is the distance from the centre of the lens to the principal focus (focal point). For a converging lens, this is the point where parallel rays of light (entering along the principal axis) actually converge after passing through the lens. For a diverging lens, the principal focus is the point from which the diverging rays appear to originate.
Focal length is measured in metres (m). A shorter focal length means a more strongly curved lens that bends light more sharply.
What is the power of a lens?
The power of a lens (P) is defined as the reciprocal of the focal length:
$$P = \frac{1}{f}$$
where P is in dioptres (D) and f is in metres (m).
- A converging lens with f = 0.25 m has P = 1 ÷ 0.25 = +4 D (positive, because it converges light).
- A diverging lens with f = 0.5 m has P = 1 ÷ 0.5 = −2 D (negative, because it diverges light).
Worked example: A camera lens has a focal length of 50 mm. Calculate its power. Convert focal length to metres: f = 50 mm = 0.050 m P = 1 ÷ 0.050 = +20 D
How do you draw ray diagrams for a converging lens?
Three standard rays are used to locate an image:
- Ray 1 — parallel to the principal axis: enters the lens parallel to the axis; after passing through the lens, it refracts and passes through the focal point on the other side.
- Ray 2 — through the optical centre: passes straight through the centre of the lens with no change in direction (it is undeviated).
- Ray 3 — through the near focal point: enters the lens heading toward the near focal point (on the same side as the object); after passing through the lens, it exits parallel to the principal axis.
Where any two of these rays cross on the other side of the lens, that is where the real image forms. Draw the image as an arrow from the principal axis to the crossing point.
What is the difference between real and virtual images?
| Feature | Real image | Virtual image |
|---|---|---|
| How formed | Rays actually converge and cross | Rays diverge — only appear to come from a point |
| Can it be projected? | Yes — on a screen | No — cannot be projected |
| Which side of lens? | Opposite side from the object | Same side as the object |
| Image orientation | Usually inverted (upside down) | Upright |
| Example | Camera sensor, cinema projector screen | Magnifying glass, wing mirror, eye |
For a converging lens:
- Object beyond focal length → real, inverted image on the other side.
- Object between lens and focal point → virtual, upright, magnified image on the same side as the object (this is how a magnifying glass works).
For a diverging lens: always produces a virtual, upright, diminished image on the same side as the object.
How are lenses used to correct eyesight problems?
The human eye contains a converging lens (the cornea and eye lens together). Focusing problems arise when the image forms in front of or behind the retina:
Short-sightedness (myopia): The eye lens system is too converging — the focal point falls in front of the retina. Distant objects appear blurred. Corrected by a diverging lens (negative power) in spectacles or contact lenses, which spreads the rays slightly before they enter the eye, moving the focal point backward onto the retina.
Long-sightedness (hyperopia): The eye lens is not converging enough — the focal point would fall behind the retina. Near objects appear blurred. Corrected by a converging lens (positive power), which pre-converges the rays slightly before they enter the eye.
| Condition | Fault | Correction | Lens type |
|---|---|---|---|
| Short-sightedness | Image forms in front of retina | Diverge rays before entering eye | Diverging, negative power |
| Long-sightedness | Image forms behind retina | Converge rays before entering eye | Converging, positive power |
Frequently asked questions
What is the difference between a converging and a diverging lens?
A converging (convex) lens is thicker in the middle and brings parallel rays of light to a real focal point on the far side of the lens, forming real images that can be projected onto a screen. A diverging (concave) lens is thinner in the middle and spreads parallel rays outward, so they appear to come from a virtual focal point on the same side as the incoming light. Converging lenses have positive power; diverging lenses have negative power.
How do you calculate the power of a lens?
The power of a lens is P = 1 ÷ f, where P is in dioptres (D) and the focal length f must be in metres. A shorter focal length means a more powerful lens. Converging lenses have positive power (they converge light); diverging lenses have negative power (they diverge light). For example, a converging lens with f = 0.2 m has P = 1 ÷ 0.2 = +5 D, while a diverging lens with f = 0.25 m has P = −4 D.
When does a converging lens produce a virtual image?
A converging lens produces a virtual, upright, and magnified image when the object is placed between the lens and the focal point — closer to the lens than one focal length. In this situation, the refracted rays diverge after leaving the lens and do not cross on the other side; instead they appear to come from a point on the same side as the object. This is the principle of a magnifying glass: the object (the text you are reading) is placed just inside the focal length, producing a magnified virtual image that the eye can see.
Which lens corrects short-sightedness and why?
Short-sightedness (myopia) is corrected by a diverging lens (negative power). In a short-sighted eye, the cornea and eye lens are together too converging, bringing light rays to a focus before they reach the retina. A diverging lens placed in front of the eye spreads the incoming rays slightly apart before they enter, reducing the overall converging power of the optical system and moving the focal point back onto the retina, where a sharp image forms.
For Socratic GCSE physics with Professor Newton — predict where the image forms before drawing any ray diagram — visit aitutors.me.