3.2.3 Thin Lenses
Objective
Describe how a thin converging (convex) lens and a thin diverging (concave) lens act on a parallel beam of light, use the correct terminology and draw the required ray diagrams, and relate the results to the lens formula.
Key Definitions & Sign Conventions
- Thin lens: thickness is negligible compared with its focal length.
- Principal axis: straight line through the optical centre of the lens, perpendicular to the lens surfaces.
- Optical centre (O): geometric centre of a thin lens; a ray passing through O is not deviated.
- Focal length (f):
- Distance from O to the principal focus.
- Positive (f > 0) for converging (convex) lenses.
- Negative (f < 0) for diverging (concave) lenses.
- Principal focus (F):
- Converging lens – real focus on the side opposite the incoming light.
- Diverging lens – virtual focus on the same side as the incoming light (rays appear to diverge from it).
- Real image: formed where actual refracted rays meet; can be projected on a screen.
- Virtual image: formed where the extensions of refracted rays appear to meet; cannot be captured on a screen.
Action on a Parallel Beam of Light
Converging (Convex) Lens
- All rays parallel to the principal axis are refracted so that they meet at the real principal focus F on the far side of the lens.
- The distance OF equals the focal length f (positive).
- If a screen is placed at F, a sharp point of light is obtained.
Diverging (Concave) Lens
- Rays parallel to the principal axis are refracted away from the axis; when extended backward they appear to diverge from the virtual principal focus F′ on the same side as the incoming light.
- The distance OF′ equals |f|, but the focal length is taken as negative (f < 0) in calculations.
- No real focus is formed on the far side; the emergent beam remains divergent.
Ray‑Diagram Construction for a Parallel Beam
- Parallel ray: Draw a ray parallel to the principal axis. After the lens it passes through the real focus (convex) or, when traced backward, through the virtual focus (concave).
- Central ray: Draw a ray through the optical centre O. This ray continues in a straight line, undeviated.
- Focal ray (optional):
- Convex lens – draw a ray aimed toward the real focus on the object side; after the lens it emerges parallel to the axis.
- Concave lens – draw a ray that emerges parallel to the axis; tracing it backward passes through the virtual focus.
- The point where the refracted rays (or their extensions) intersect gives the image position.
Lens Formula Reminder
When a numerical answer is required, use the thin‑lens equation
1/f = 1/v + 1/u
where u is the object distance (negative if the object is on the same side as the incoming light), v is the image distance (positive for real images on the far side, negative for virtual images on the same side), and f follows the sign convention given above.
Image Characteristics for a Converging Lens
| Object Position | Relation to f | Image type | Image location (v) | Orientation | Size |
|---|
| Beyond 2f (far away) | u > 2f | Real | Between f and 2f on the far side | Inverted | Reduced |
| At 2f | u = 2f | Real | At 2f on the far side | Inverted | Same size as object |
| Between f and 2f | f < u < 2f | Real | Beyond 2f on the far side | Inverted | Enlarged |
| At f | u = f | None (rays emerge parallel) | Image at infinity | — | — |
| Between lens and f | u < f | Virtual | Same side as the object, between lens and f | Upright | Enlarged |
Image Characteristics for a Diverging Lens (All Object Positions)
- Image is always virtual, upright and reduced.
- It forms on the same side of the lens as the object, between the lens and the virtual focus F′.
- Diverging lenses never produce a real image, even for objects at infinity.
Typical Applications (Optional Extension)
- Camera objective – a converging lens forms a real, inverted image of a distant scene on the film or sensor.
- Magnifying glass – a converging lens used with the object placed between the lens and its focal point; the virtual, upright, enlarged image is viewed directly.
- Eyeglasses:
- Convex lenses for farsighted (hyperopic) people.
- Concave lenses for nearsighted (myopic) people.
- Telescope (Keplerian) – combination of a large converging objective lens and a smaller converging eyepiece lens.
Optional: Lens‑Maker’s Equation (Extended Content)
For lenses made from a material of refractive index n and with radii of curvature R₁ and R₂, the focal length is given by
\( \displaystyle \frac{1}{f}= (n-1)\left(\frac{1}{R{1}}-\frac{1}{R{2}}\right) \)
This equation is useful for designing lenses but is not required for the IGCSE exam.
Exam Checklist (IGCSE 0625)
- State the sign convention clearly: f > 0 for converging, f < 0 for diverging lenses.
- For a parallel beam:
- Converging lens → real focus on the far side.
- Diverging lens → virtual focus on the same side; never a real image.
- When drawing a ray diagram always include the parallel ray and the central ray (add the focal ray if you wish).
- Identify the image type (real/virtual), location (use the lens formula if required), orientation (inverted/upright) and size (reduced/enlarged).
- Remember the special case for a converging lens when the object is at the focal point – the image is at infinity and the emergent rays are parallel.
- For a magnifying‑glass situation, note that the object is between the lens and its focal point, giving a virtual, upright, enlarged image.