Converging (Convex) Lenses

This lesson covers converging (convex) lenses as required by the Edexcel GCSE Physics specification (1PH0), Topic 5: Light and the Electromagnetic Spectrum. You need to understand focal point, focal length, how to draw ray diagrams, and how the position of the object determines the type of image formed.

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What Is a Converging Lens?

A converging lens (also called a convex lens) is thicker in the middle than at the edges. It causes parallel rays of light to converge (come together) to a single point called the focal point (or principal focus).

Key Definitions

Term	Definition
Converging lens	A lens that is thicker in the middle; it brings parallel rays of light to a focus
Principal axis	The horizontal line passing through the centre of the lens
Focal point (F)	The point where parallel rays of light converge after passing through the lens
Focal length (f)	The distance from the centre of the lens to the focal point
2F	A point at twice the focal length from the centre of the lens
Optical centre	The centre of the lens — rays passing through here are not deviated

Exam Tip: There is a focal point on each side of the lens, both at the same distance from the centre. When drawing ray diagrams, you need to mark F and 2F on both sides of the lens.

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The Three Standard Rays for Ray Diagrams

When drawing ray diagrams for a converging lens, you should use at least two of these three standard rays:

1. A ray parallel to the principal axis → after passing through the lens, it refracts and passes through the focal point (F) on the far side.
2. A ray passing through the focal point (F) on the near side → after passing through the lens, it refracts and travels parallel to the principal axis.
3. A ray passing through the optical centre of the lens → it passes straight through without changing direction.

The point where two (or more) of these rays meet on the far side of the lens is where the image is formed.

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Image Formation — Different Object Positions

The type of image formed depends on where the object is placed relative to the focal point (F) and 2F.

Object Beyond 2F (far from lens)

Property	Description
Image position	Between F and 2F on the other side
Image type	Real
Orientation	Inverted (upside down)
Size	Diminished (smaller than the object)
Application	Camera, the eye

Object at 2F

Property	Description
Image position	At 2F on the other side
Image type	Real
Orientation	Inverted
Size	Same size as the object

Object Between F and 2F

Property	Description
Image position	Beyond 2F on the other side
Image type	Real
Orientation	Inverted
Size	Magnified (larger than the object)
Application	Projector

Object at F

Property	Description
Image position	At infinity (rays are parallel after the lens)
Image type	No image formed
Use	Searchlight, spotlight beam

Object Between F and the Lens

Property	Description
Image position	On the same side as the object (behind it)
Image type	Virtual
Orientation	Upright
Size	Magnified
Application	Magnifying glass

flowchart TD
    A["Object beyond 2F"] --> B["Image: between F and 2F<br/>Real, inverted, diminished"]
    C["Object at 2F"] --> D["Image: at 2F<br/>Real, inverted, same size"]
    E["Object between F and 2F"] --> F["Image: beyond 2F<br/>Real, inverted, magnified"]
    G["Object at F"] --> H["No image formed<br/>Rays emerge parallel"]
    I["Object between F and lens"] --> J["Image: same side as object<br/>Virtual, upright, magnified"]

    style A fill:#2c3e50,color:#fff
    style C fill:#2c3e50,color:#fff
    style E fill:#2c3e50,color:#fff
    style G fill:#2c3e50,color:#fff
    style I fill:#2c3e50,color:#fff
    style B fill:#3498db,color:#fff
    style D fill:#3498db,color:#fff
    style F fill:#3498db,color:#fff
    style H fill:#e74c3c,color:#fff
    style J fill:#27ae60,color:#fff

Exam Tip: Learn the mnemonic "Beyond 2F → diminished; Between F and 2F → magnified; Beyond F → virtual". When describing an image, always state three things: (1) real or virtual, (2) upright or inverted, (3) magnified, diminished, or same size.

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Magnification

Magnification tells you how much larger (or smaller) the image is compared to the object.

$\text{Magnification} = \frac{\text{image height}}{\text{object height}}$Magnification=object heightimage height​

Magnification can also be calculated using distances:

$\text{Magnification} = \frac{v}{u}$Magnification=uv​

Where:

• v = distance from the lens to the image (image distance)
• u = distance from the lens to the object (object distance)

Key Points

• Magnification has no units — it is a ratio.
• If magnification > 1, the image is magnified (larger).
• If magnification < 1, the image is diminished (smaller).
• If magnification = 1, the image is the same size.

Worked Example

An object is 3.0 cm tall and the image formed by a converging lens is 9.0 cm tall. Calculate the magnification.

$\text{Magnification} = \frac{\text{image height}}{\text{object height}} = \frac{9.0}{3.0} = 3.0$Magnification=object heightimage height​=3.09.0​=3.0

The magnification is 3.0 — the image is 3 times larger than the object.

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Power of a Lens (Higher Tier)

The power of a lens measures how strongly it converges (or diverges) light. It is related to the focal length.

$\text{Power} = \frac{1}{f}$Power=f1​

Where:

• Power is measured in dioptres (D)
• f = focal length in metres

Key Points

• A short focal length means a powerful lens (bends light more).
• A long focal length means a weak lens (bends light less).
• Converging lenses have positive power values.
• Diverging lenses have negative power values.

Worked Example

A converging lens has a focal length of 20 cm. Calculate its power.

Step 1: Convert focal length to metres: f = 20 cm = 0.20 m

Step 2: Calculate power:

$P = \frac{1}{f} = \frac{1}{0.20} = +5.0 \text{ D}$P=f1​=0.201​=+5.0 D

The power of the lens is +5.0 D.

Exam Tip: Remember to convert the focal length to metres before calculating power. A focal length of 25 cm = 0.25 m, not 25. Also, include the positive sign for converging lenses and the negative sign for diverging lenses.

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Applications of Converging Lenses

Application	Object Position	Image Type
Magnifying glass	Between F and the lens	Virtual, upright, magnified
Camera	Beyond 2F	Real, inverted, diminished
Projector	Between F and 2F	Real, inverted, magnified (projected onto screen)
The human eye	Beyond 2F	Real, inverted, diminished (on retina)

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Summary