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 thin-lens equation predicts distances within the paraxial model.

This lesson supports Chapter 22 of High School Physics.

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 and rays close to the optical axis, \[\frac1f=\frac1{d_o}+\frac1{d_i}.\] Magnification is \(m=\frac{h_i}{h_o}=-\frac{d_i}{d_o}\). 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 \(\frac1{d_i}=\frac1{10}-\frac1{30}=\frac1{15}\), 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. \(\frac1f=\frac1{d_o}+\frac1{d_i}\).
3. \(m=-\frac{d_i}{d_o}\).
4. No.
5. An objective and an eyepiece.
6. It changes the shape of its lens.

Keep studying

High School Physics includes 12 full-length practice tests: two in the book and ten online.

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