Recall that visible light of a single frequency is described as monochromatic
3.2.3 Thin Lenses
What are thin lenses? A thin lens is a lens whose thickness is small compared to its focal length. Think of it like a magnifying glass that is so thin you can almost see through it. Thin lenses are used in glasses, cameras, microscopes, and many everyday devices.
Key Concepts
- Focal length ($f$) – the distance from the lens where parallel rays converge (converging lens) or appear to diverge from (diverging lens).
- Object distance ($d_o$) – distance from the object to the lens.
- Image distance ($d_i$) – distance from the image to the lens.
- Thin‑lens formula: $$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$
- Magnification ($m$): $$m = \frac{h_i}{h_o} = -\frac{d_i}{d_o}$$ – negative sign indicates image inversion.
- Real vs. virtual images: Real images can be projected on a screen; virtual images cannot.
- Monochromatic light – light of a single frequency (colour) behaves the same through a lens, so we ignore chromatic aberration in basic calculations.
Lens Formula in Action
| Scenario | Given | Result |
|---|---|---|
| Converging lens, object beyond focal point | $f = 10\,\text{cm}$, $d_o = 30\,\text{cm}$ | $d_i = 15\,\text{cm}$ (real, inverted) |
| Diverging lens, object anywhere | $f = -12\,\text{cm}$, $d_o = 20\,\text{cm}$ | $d_i = -7.5\,\text{cm}$ (virtual, upright) |
Image Formation Examples
🔍 Example 1 – A book in front of a magnifying glass: The book is 25 cm from the lens, the lens has a focal length of 10 cm. Using the thin‑lens formula, the image forms at 16.7 cm on the other side. The image is real and inverted, but because the lens is close to the book, we see a magnified, upright virtual image when we look through the lens.
📐 Example 2 – A camera lens: A camera sensor is 2 cm from the lens. If we want a sharp image of a distant object (effectively at infinity), the lens must be positioned at its focal length, e.g., $f = 2\,\text{cm}$.
Monochromatic Light in Lens Experiments
When we use a laser pointer (a single frequency of light), the lens behaves predictably because all rays have the same wavelength. This eliminates chromatic aberration, so the image is sharp and colour‑consistent. In contrast, white light contains many frequencies, which can spread out slightly after passing through a lens.
Exam Tips 🎯
- Always write down the sign convention: $f$ positive for converging, negative for diverging.
- Check units – keep all distances in the same units (cm or m).
- Use the magnification formula to find image height if needed.
- Remember: a real image is inverted, a virtual image is upright.
- For monochromatic light questions, you can ignore chromatic aberration unless the question explicitly asks for it.
- Sketch the ray diagram – it often helps to spot mistakes.
Revision
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