3.2.3 Thin lenses
- Syllabus
- 0625–2026–2027
- Topic
- 3.2.3
- Level
- —
Learning objectives
3.2.3.1Action of thin converging and thin• Describe the action of thin converging and thin diverging lenses on a parallel beam of light3.2.3.2Terms focal length, principal axis and• Define and use the terms focal length, principal axis and principal focus (focal point)3.2.3.3Ray diagrams for the formation of a• Draw and use ray diagrams for the formation of a real image by a converging lens3.2.3.4Characteristics of an image using the• Describe the characteristics of an image using the terms enlarged/same size/diminished, upright/inverted and real/virtual3.2.3.5A virtual image is formed when• Know: a virtual image is formed when diverging rays are extrapolated backwards and does not form a visible projection on a screen3.2.3.6Ray diagrams for the formation of a• Draw and use ray diagrams for the formation of a virtual image by a converging lens3.2.3.7Use of a single lens as a magnifying• Describe the use of a single lens as a magnifying glass3.2.3.8Use of converging and diverging lenses• Describe the use of converging and diverging lenses to correct long-sightedness and short-sightedness
Compare converging and diverging lenses
A thin converging lens bends a parallel beam towards the principal axis so the rays meet at the principal focus. A thin diverging lens bends the beam away from the principal axis.
| Lens | Shape | Action on a parallel beam | Principal focus |
|---|---|---|---|
| converging | thicker at the centre | rays converge after the lens | real focus on the far side |
| diverging | thinner at the centre | rays spread out after the lens | virtual focus on the incident side, found by extending the rays backwards |
A lens that changes the ray directions more strongly has a shorter focal length. A thinner converging lens is usually weaker and therefore has a longer focal length than a thicker one made from the same material.
Only rays incident parallel to the principal axis pass through, or appear to come from, the principal focus. An arbitrary ray is not forced through that point.
Define the axis, focus and focal length
The principal axis is the straight line through the optical centre of the lens and perpendicular to the lens plane.
| Term | Meaning for a thin converging lens |
|---|---|
| principal focus, F | point on the principal axis where rays initially parallel to the axis meet after refraction |
| focal length, f | distance from the optical centre of the lens to a principal focus |
| two principal focuses | one focus lies on each side of a thin lens, the same distance from its optical centre |
To mark the focuses for a lens of focal length f, measure f along the principal axis from the optical centre on both sides. The focal length is a lens-to-focus distance, not an object-to-image distance.
A focus is a point, whereas focal length is a distance. The principal axis passes through the optical centre; it is not any convenient horizontal line in a sketch.
Construct a real image with two rays
A converging lens forms a real image when the object is farther from the lens than one focal length. The refracted rays actually meet on the opposite side of the lens.
| Start at the top of the object | Continue after the lens |
|---|---|
| ray parallel to the principal axis | through the far principal focus |
| ray through the optical centre | straight on without changing direction in the thin-lens model |
| ray through the near principal focus | parallel to the principal axis |
Draw any two standard rays accurately. Their actual intersection fixes the top of the image; draw the image arrow from the principal axis to that point. Use the completed geometry to measure image position, size or focal length when the diagram is to scale.
Do not extend refracted rays backwards for a real image. The solid outgoing rays themselves must cross, and a screen placed at that crossing can receive a sharp image.
Describe every lens image with three properties
Describe a lens image with three independent comparisons: size, orientation and type.
| Comparison | Allowed terms | Test |
|---|---|---|
| size | enlarged, same size, diminished | compare image height with object height |
| orientation | upright, inverted | compare which way the image points |
| type | real, virtual | decide whether actual rays meet and whether the image can be projected |
| Object position for a converging lens | Image description |
|---|---|
| beyond 2f | diminished, inverted, real |
| at 2f | same size, inverted, real |
| between f and 2f | enlarged, inverted, real |
| inside f | enlarged, upright, virtual |
Enlarged does not imply virtual: an object between f and 2f gives an enlarged real image. Real images made by one converging lens are inverted; the magnifying-glass image is upright and virtual.
Distinguish real and virtual images
A real image forms where light rays actually converge. It can be received as a visible projection on a screen placed at the image position.
A virtual image forms where diverging rays appear to come from when their paths are extrapolated backwards. No light rays actually pass through that apparent image position, so it cannot be projected onto a screen.
| Diagram evidence | Image type |
|---|---|
| solid rays meet at the image | real |
| solid rays diverge but dashed backward extensions meet | virtual |
| a sharp image appears on a screen | real |
| image is seen only by looking into the outgoing rays | virtual |
Virtual does not mean invisible: an eye can see a virtual image because light enters the eye along directions that appear to originate from it. The missing property is screen projection, not visibility to an observer.
Construct the virtual image from a converging lens
Place the object between a converging lens and its near principal focus. The emerging rays diverge, so the image is virtual, upright and enlarged on the same side of the lens as the object.
| Start at the top of the object | Continue after the lens |
|---|---|
| ray parallel to the principal axis | through the far focus |
| ray through the optical centre | straight on |
| ray directed towards the near focus before the lens | parallel to the principal axis |
Draw two outgoing rays with solid lines. Because they spread apart, extend them backwards behind the object with dashed lines. Their backward intersection gives the top of the virtual image; draw an upright image arrow to the principal axis.
The dashed extensions show apparent origin only and are not paths travelled by light. If the object is beyond the focal point, the construction changes to an actual, inverted real-image intersection on the far side.
Use a converging lens as a magnifying glass
A magnifying glass is a single converging lens with the object placed between the lens and its principal focus. The observer looks through the lens from the opposite side.
The lens sends diverging rays into the eye. The eye traces those rays backwards to a larger upright image on the same side of the lens as the object, so the image is enlarged, upright and virtual.
| Adjustment | Result |
|---|---|
| keep object distance less than f | maintains a virtual upright image |
| move lens or object while looking through it | finds a clear enlarged view |
| place a screen at the apparent image | no sharp projection forms because the image is virtual |
An object at the principal focus gives emerging parallel rays and an image effectively at infinity; it is not the only possible magnifying-glass position. The working object position is inside one focal length.
Correct long- and short-sightedness
A correcting spectacle lens changes the vergence of incoming light before it reaches the eye so that the eye lens focuses the final image on the retina.
| Vision defect | Uncorrected focus for a distant or near target | Correcting lens | Action |
|---|---|---|---|
| short-sightedness | in front of the retina, especially for distant objects | diverging lens | spreads incoming rays so the eye's converging system focuses them farther back, on the retina |
| long-sightedness | behind the retina, especially for near objects | converging lens | pre-converges incoming rays so the eye focuses them sooner, on the retina |
A diverging spectacle lens is thinner at the centre; a converging spectacle lens is thicker at the centre. In either correction, the required final condition is a sharp focus on the retina.
Do not match the lens name to the defect by shape alone. First locate the uncorrected focus: in front of the retina needs divergence; behind the retina needs extra convergence.