Diverging (Concave) Lenses

This lesson covers diverging (concave) lenses as required by the Edexcel GCSE Physics specification (1PH0), Topic 5: Light and the Electromagnetic Spectrum. You need to understand how diverging lenses form images, how to draw ray diagrams, and the differences between converging and diverging lenses.

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What Is a Diverging Lens?

A diverging lens (also called a concave lens) is thinner in the middle than at the edges. It causes parallel rays of light to spread out (diverge) as if they came from a single point behind the lens — the virtual focal point.

Key Definitions

Term	Definition
Diverging lens	A lens that is thinner in the middle; it spreads parallel rays of light apart
Virtual focal point (F)	The point from which the diverging rays appear to come (on the same side as the incoming light)
Focal length (f)	The distance from the centre of the lens to the virtual focal point

Exam Tip: The focal point of a diverging lens is on the same side as the incoming light. The rays do not actually pass through this point — they only appear to come from it. That is why it is called a virtual focal point.

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Ray Diagrams for Diverging Lenses

To draw a ray diagram for a diverging lens, use at least two of these three standard rays:

1. A ray parallel to the principal axis → after passing through the lens, it diverges as if it came from the virtual focal point (F) on the near side.
2. A ray directed towards the focal point (F) on the far side → after passing through the lens, it travels parallel to the principal axis.
3. A ray passing through the optical centre → passes straight through without changing direction.

How to Locate the Image

The refracted rays diverge after passing through the lens, so they never actually meet on the far side. To find the image, you must extend the refracted rays backwards (as dashed lines). The point where these extended rays meet is where the virtual image is formed.

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The Image Formed by a Diverging Lens

No matter where the object is placed, a diverging lens always produces the same type of image:

Property	Description
Image type	Virtual
Orientation	Upright (same way up as the object)
Size	Diminished (smaller than the object)
Position	On the same side as the object, between F and the lens

This is very different from a converging lens, where the image type depends on the object position.

Exam Tip: A diverging lens always forms a virtual, upright, diminished image — regardless of where the object is. This makes it simpler to remember than a converging lens. If the exam asks about a concave/diverging lens, the answer is always the same three words: virtual, upright, diminished.

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Power of a Diverging Lens (Higher Tier)

The power of a diverging lens is calculated using the same formula as for a converging lens:

$P = \frac{1}{f}$P=f1​

However, the focal length of a diverging lens is given a negative value by convention, so the power is also negative.

Worked Example

A diverging lens has a focal length of 50 cm. Calculate its power.

Step 1: Convert to metres and apply the negative sign: f = −0.50 m

Step 2: Calculate power:

$P = \frac{1}{f} = \frac{1}{-0.50} = -2.0 \text{ D}$P=f1​=−0.501​=−2.0 D

The power of the lens is −2.0 D.

Exam Tip: The negative sign is essential. Converging lenses have positive power; diverging lenses have negative power. If a question mentions a negative power or negative focal length, it is a diverging lens.

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Comparing Converging and Diverging Lenses

Feature	Converging (Convex) Lens	Diverging (Concave) Lens
Shape	Thicker in the middle	Thinner in the middle
Effect on parallel rays	Brings them together to a focus	Spreads them apart
Focal point	Real (rays pass through it)	Virtual (rays appear to come from it)
Types of image	Real or virtual (depends on object position)	Always virtual
Image orientation	Can be inverted or upright	Always upright
Image size	Can be magnified, diminished, or same size	Always diminished
Power	Positive (+)	Negative (−)

flowchart LR
    A["Parallel rays<br/>of light"] --> B["CONVERGING LENS<br/>(thicker in middle)"]
    B --> C["Rays converge<br/>to focal point F<br/>(real focus)"]
    D["Parallel rays<br/>of light"] --> E["DIVERGING LENS<br/>(thinner in middle)"]
    E --> F["Rays diverge apart<br/>appearing to come<br/>from virtual F"]

    style B fill:#27ae60,color:#fff
    style E fill:#e74c3c,color:#fff
    style C fill:#27ae60,color:#fff
    style F fill:#e74c3c,color:#fff

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Applications of Diverging Lenses

1. Correcting Short-Sightedness (Myopia)

The most important application of diverging lenses is in correcting short-sightedness. A short-sighted person's eye focuses distant objects in front of the retina (the eye is too long or the lens is too powerful). A diverging lens placed in front of the eye spreads the light rays slightly before they enter the eye, allowing the eye to focus the image onto the retina correctly.

2. Peepholes (Door Viewers)

A peephole in a front door uses a diverging lens. It gives a wide-angle, diminished view of the area outside the door, allowing the occupant to see who is there.

3. Combined Lens Systems

Diverging lenses are often used in combination with converging lenses in devices such as cameras and telescopes to correct for lens aberrations and improve image quality.

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Worked Example — Identifying Lens Type from an Image

A student places an object in front of a lens and observes that the image is virtual, upright, and smaller than the object. What type of lens is being used?

The image is virtual, upright, and diminished. These are the properties of an image formed by a diverging (concave) lens. A converging lens can produce a virtual, upright image, but that image would be magnified, not diminished. Therefore the lens must be diverging.

Exam Tip: If you are given image properties and asked to identify the lens, remember: a virtual, upright, diminished image = diverging lens. A virtual, upright, magnified image = converging lens (with the object between F and the lens).

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Summary