Describe the use of a single lens as a magnifying glass
3.2.3 Thin Lenses – Using a Lens as a Magnifying Glass
🔍 What is a Magnifying Glass?
A magnifying glass is simply a single convex lens that lets you see small objects more clearly by making them appear larger. Think of it as a “zoom‑in” button for your eyes.
📐 How Does It Work?
When you place an object within the near point (usually 25 cm from your eye), a convex lens creates a real, inverted image that is farther away. Your eye then focuses on this image as if it were at the near point, making the object look larger.
- Object distance u is < 25 cm.
- Lens produces an image at distance v (real, inverted).
- Eye focuses on the image at the near point, giving a magnified view.
Key equations:
| Formula | Meaning |
|---|---|
| $\displaystyle \frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ | Lens formula – relates focal length f, object distance u, and image distance v. |
| $m = -\frac{v}{u}$ | Magnification – negative sign shows the image is inverted. |
| $m_{\text{angular}} = \frac{25\,\text{cm}}{f}$ | Angular magnification when the image is at the near point. |
💡 Example: A 10 cm Lens
Suppose you have a convex lens with focal length $f = 10\,\text{cm}$. You place a coin 15 cm from the lens.
- Calculate image distance: $\displaystyle \frac{1}{10} = \frac{1}{v} + \frac{1}{15} \;\Rightarrow\; v \approx 6\,\text{cm}$.
- Magnification: $m = -\frac{6}{15} \approx -0.4$ (the image is smaller and inverted).
- To use it as a magnifier, move the coin to < 10 cm so that the image is beyond 25 cm, giving a larger apparent size.
Remember: the closer the object to the lens (but still > $f$), the larger the magnification.
📚 Exam Tips
- Always state the near point (25 cm) when calculating angular magnification.
- Use the lens formula to find image distance before applying magnification.
- Check the sign of $m$ – a negative value means the image is inverted.
- When asked to design a magnifier, choose a lens with a small focal length (e.g., 5–10 cm) for higher magnification.
- Remember that the magnifying glass works best when the image is at the near point; otherwise, the eye has to adjust focus.
🎓 Quick Practice Question
Given a convex lens with $f = 8\,\text{cm}$, an object is placed 12 cm from the lens. What is the angular magnification if the image is at the near point?
Answer: First find $v$ using $\displaystyle \frac{1}{8} = \frac{1}{v} + \frac{1}{12}$ → $v \approx 4.8\,\text{cm}$. Since $v$ < 25 cm, the image is not at the near point. To make it at 25 cm, adjust $u$ accordingly. Once $v = 25\,\text{cm}$, $m_{\text{angular}} = \frac{25}{8} \approx 3.1$.
Use this method to solve similar problems quickly!
Revision
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