What you'll learn
This revision guide covers how lenses manipulate visible light through refraction to form images. You'll learn to distinguish between converging and diverging lenses, construct accurate ray diagrams, and understand the characteristics of images formed by different lens types. These concepts are essential for understanding cameras, magnifying glasses, and corrective eyewear.
Key terms and definitions
Lens — a shaped piece of transparent material (usually glass or plastic) that refracts light
Converging lens (convex lens) — a lens that is thicker in the middle than at the edges and causes parallel rays of light to converge (come together) at the principal focus
Diverging lens (concave lens) — a lens that is thinner in the middle than at the edges and causes parallel rays of light to diverge (spread out) as if from the principal focus
Principal focus (focal point) — the point where rays parallel to the principal axis converge after passing through a converging lens, or appear to diverge from in a diverging lens
Focal length — the distance from the centre of the lens to the principal focus
Principal axis — an imaginary line passing through the centre of the lens at right angles to its surface
Real image — an image formed where light rays actually meet and can be projected onto a screen
Virtual image — an image formed where light rays appear to come from but do not actually meet; cannot be projected onto a screen
Core concepts
Types of lenses and their properties
Lenses work by refracting light as it passes through them. The curved surfaces cause light rays to change direction.
Converging (convex) lenses:
- Bulge outwards in the middle
- Thicker at the centre than at the edges
- Cause parallel rays to converge at the principal focus
- Can form both real and virtual images depending on object position
- Used in cameras, telescopes, and magnifying glasses
Diverging (concave) lenses:
- Curve inwards in the middle
- Thinner at the centre than at the edges
- Cause parallel rays to spread out (diverge)
- Always form virtual, upright, diminished images
- Used to correct short-sightedness and in some optical instruments
Each lens has two principal foci, one on each side, equidistant from the lens centre. For a converging lens, the focal length is the distance where parallel rays actually meet. For a diverging lens, it's the distance from where the rays appear to originate.
Refraction in lenses
Light refracts (changes direction) when it enters and exits a lens because of the change in speed as it moves between air and glass.
In a converging lens:
- Light slows down entering the glass
- Rays bend towards the normal at the first surface
- Rays bend away from the normal at the second surface
- The net effect causes rays to converge
In a diverging lens:
- Light also slows entering the glass
- The shape of the lens surfaces causes rays to bend in a way that spreads them out
- The net effect causes rays to diverge
The amount of refraction depends on:
- The curvature of the lens surfaces (more curved = more powerful)
- The refractive index of the lens material
- The angle at which light hits the surface
Ray diagrams for converging lenses
Ray diagrams help predict where images form. For accuracy, you need to draw at least two of these three construction rays:
Ray 1: A ray parallel to the principal axis refracts through the lens and passes through the principal focus on the far side
Ray 2: A ray passing through the centre of the lens continues in a straight line without deviation (it enters and exits at parallel surfaces)
Ray 3: A ray passing through the principal focus on the near side refracts through the lens and emerges parallel to the principal axis
Where the rays meet (or appear to meet) is where the image forms.
Object beyond 2F (twice the focal length):
- Image forms between F and 2F on the opposite side
- Image is real, inverted, and diminished
- Example: camera
Object at 2F:
- Image forms at 2F on the opposite side
- Image is real, inverted, and same size
- Example: some photocopiers
Object between F and 2F:
- Image forms beyond 2F on the opposite side
- Image is real, inverted, and magnified
- Example: projector
Object at F:
- Rays emerge parallel
- No image forms (or image at infinity)
Object inside F (closer than focal length):
- Rays diverge after the lens
- Image forms on the same side as the object
- Image is virtual, upright, and magnified
- Example: magnifying glass
Ray diagrams for diverging lenses
Diverging lenses always produce the same type of image regardless of object position.
Construction rays for diverging lenses:
Ray 1: A ray parallel to the principal axis refracts and appears to come from the principal focus on the same side as the object
Ray 2: A ray passing through the centre of the lens continues straight
Ray 3: A ray heading towards the principal focus on the far side refracts and emerges parallel to the principal axis
The rays diverge after passing through the lens, so they don't actually meet. Trace the rays backwards (using dotted lines) to find where they appear to come from.
For any object position:
- Image forms on the same side as the object
- Image is virtual, upright, and diminished
- Image is always between the lens and the principal focus
- The closer the object is to the lens, the larger the image
Image characteristics and terminology
When describing images formed by lenses, you must specify four characteristics:
Position: Where the image is located relative to the lens (give distances if measured)
Nature: Real or virtual
- Real images can be projected onto screens
- Virtual images cannot be projected
Orientation: Upright or inverted (upside down) relative to the object
Size: Magnified (larger), diminished (smaller), or same size compared to the object
The magnification of an image can be calculated:
magnification = image height ÷ object height
Or alternatively:
magnification = image distance ÷ object distance
A magnification greater than 1 means the image is larger than the object. A magnification less than 1 means the image is smaller.
Applications of lenses
Converging lenses:
- Cameras: Object is beyond 2F, producing a real, inverted, diminished image on the film or sensor
- Projectors: Object is between F and 2F, producing a real, inverted, magnified image on screen
- Magnifying glasses: Object is within F, producing a virtual, upright, magnified image
- Correcting long-sightedness: A converging lens helps focus light from close objects onto the retina
Diverging lenses:
- Correcting short-sightedness: A diverging lens spreads out light rays before they enter the eye, moving the focal point back onto the retina
- Peepholes in doors: Produce a wide-angle, diminished view
- Used in combination with converging lenses in compound optical instruments like cameras and telescopes to reduce aberrations
Worked examples
Example 1: Ray diagram for a converging lens
Question: An object is placed 15 cm from a converging lens with a focal length of 5 cm. Draw a ray diagram to show where the image forms. Describe the characteristics of the image. [6 marks]
Solution:
[In the exam, you would draw a scaled diagram. Here's the method:]
- Draw the principal axis and lens
- Mark focal points at 5 cm on each side of the lens
- Mark 2F at 10 cm on each side
- Place object at 15 cm from lens (beyond 2F)
- Draw two construction rays:
- Ray parallel to axis → refracts through far focus
- Ray through lens centre → continues straight
- Mark where rays intersect
Image characteristics:
- Position: Between F and 2F on opposite side of lens (between 5 cm and 10 cm from lens) ✓
- Nature: Real ✓
- Orientation: Inverted ✓
- Size: Diminished ✓
[2 marks for accurate ray diagram, 4 marks for characteristics]
Example 2: Magnification calculation
Question: A converging lens produces an image 24 cm tall of an object that is 4 cm tall. Calculate the magnification. [2 marks]
Solution:
magnification = image height ÷ object height ✓
magnification = 24 ÷ 4 = 6 ✓
[1 mark for correct formula, 1 mark for correct answer]
Example 3: Describing diverging lens images
Question: Explain why diverging lenses always produce virtual images, regardless of where the object is placed. [3 marks]
Solution:
Diverging lenses cause parallel rays to spread out (diverge) after passing through the lens ✓
The refracted rays never actually meet on the far side of the lens ✓
The rays appear to come from a point on the same side as the object, forming a virtual image ✓
[1 mark for each correct physics point]
Common mistakes and how to avoid them
Confusing lens types: Remember converging lenses are fatter in the middle (think "c for convex, c for curved outward"); diverging lenses are thinner in the middle. Check which way rays bend.
Drawing inaccurate ray diagrams: Always use a ruler and draw to scale where possible. Make sure rays pass through (not near) the principal focus and lens centre. Use arrows to show ray direction.
Forgetting to describe all four image characteristics: In exam questions asking you to describe an image, always state position, nature (real/virtual), orientation (upright/inverted), and size (magnified/diminished/same size).
Confusing real and virtual images: Real images form where rays actually meet and can be projected onto a screen. Virtual images form where rays appear to come from and cannot be projected.
Mixing up focal length and focal point: The focal point (or principal focus) is a location; the focal length is the distance from the lens centre to that point.
Not continuing construction rays far enough: When drawing diverging lens diagrams, you must trace rays backwards (using dotted lines) to find where they appear to originate from.
Exam technique for "Lenses and visible light (converging and diverging)"
"Draw a ray diagram" questions (4-6 marks): Use a ruler and sharp pencil. Draw at least two construction rays correctly. Label the image position. Include arrows on rays. Draw to scale if measurements are given. Check rays pass through exact points (focus, lens centre).
"Describe the image" questions (3-4 marks): Give all four characteristics systematically: position (with measurements if on diagram), real or virtual, upright or inverted, magnified/diminished/same size. Each characteristic typically earns one mark.
"Explain" command words (3-4 marks): Describe what happens to light rays (refraction direction) and link cause to effect. Use correct terminology: refract, converge, diverge, principal focus. Show logical reasoning across multiple linked statements.
Application questions: Link lens properties to real-world uses. For example, cameras need real images (to project onto sensors), while magnifying glasses need magnified images (so object must be within focal length of converging lens).
Quick revision summary
Converging (convex) lenses are thicker in the middle and bring parallel light rays together at the principal focus. They form real, inverted images when objects are beyond the focal length, and virtual, upright, magnified images when objects are inside the focal length. Diverging (concave) lenses are thinner in the middle and spread light rays apart. They always form virtual, upright, diminished images. Ray diagrams use construction rays through the focal point and lens centre to locate images. Real images can be projected; virtual images cannot.