Lenses and Optical Instruments

A lens forms an image by bending many rays in a coordinated way. A ray diagram gives the geometry, while the lens equation supplies exact distances.

This lesson supports Chapter 22 of Physics for Beginners. Keep the physical picture in view, write the units, and check the direction of every vector before trusting a calculation.

Converging and diverging lenses treat rays differently

A converging lens brings parallel rays toward a focal point. A diverging lens spreads them as if they came from a focal point on the incident side. Standard ray diagrams use rays parallel to the axis, through the focal point, and through the lens center.

The thin-lens equation connects distances

For a thin lens, \[\frac1f=\frac1{d_o}+\frac1{d_i}.\] Magnification is \(m=h_i/h_o=-d_i/d_o\). A real image can be projected onto a screen. A virtual image cannot be caught on a screen because the light rays do not actually meet there.

Optical instruments manage angular size

A magnifier produces a larger virtual image for the eye. A microscope uses an objective and eyepiece to enlarge nearby small objects. A telescope collects light from distant objects and increases their apparent angular size. The human eye changes focus by adjusting the shape of its lens.

Worked example

An object sits \(30\text{ cm}\) from a converging lens with \(f=10\text{ cm}\). Then \(1/d_i=1/10-1/30=1/15\), so \(d_i=15\text{ cm}\). The positive image distance describes a real image.

Watch the idea in action

Khan Academy gives a focused explanation of the chapter’s central idea. Pause before each calculation and predict the next step on paper.

Practice questions

1. What does a converging lens do to parallel rays?
2. Write the thin-lens equation.
3. Write the magnification relation using distances.
4. Can a virtual image be projected onto a screen?
5. What two main lenses appear in a simple microscope?
6. How does the eye focus at different distances?

Answers

1. It brings them toward a focal point.
2. \(1/f=1/d_o+1/d_i\).
3. \(m=-d_i/d_o\).
4. No.
5. An objective and an eyepiece.
6. It changes the shape of its lens.

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