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.

  1. Object distance u is < 25 cm.

  2. Lens produces an image at distance v (real, inverted).

  3. Eye focuses on the image at the near point, giving a magnified view.

Key equations:

FormulaMeaning
\$\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!