Refraction through Lenses — Part 2: Lens formula, magnification and power: visual lesson, ICSE Class 10 Physics (Science Paper 1)

Lesson

Putting numbers on images

Part 2 — ray diagrams tell us roughly where an image is; the lens formula tells us exactly. Opticians describe lenses by their power in dioptres.

In this lesson you will

Apply the New Cartesian sign convention to object and image distances
Use the lens formula and magnification in direct numerical problems
Calculate the power of a lens in dioptres with the correct sign
Describe the magnifying glass and other uses of lenses

Table of four questions about lenses and the tool that answers each
Question	Tool
Where is the image?	Lens formula
How big is it, and which way up?	Magnification
How strongly does the lens bend light?	Power in dioptres
Which way do we measure?	Sign convention

Diagram

The New Cartesian sign convention

All distances are measured from the optical centre O.
Distances measured in the direction of the incident light (left to right) are positive; those against it are negative. So a real object has u negative.
Heights above the principal axis are positive; below, negative.

Consequences: $f$ is positive for a convex lens and negative for a concave lens; a real image (other side) has v positive, a virtual image (same side) has v negative.

Concept

Lens formula and magnification

For a thin lens, with all distances in the same unit and signs from the convention: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ Linear magnification: $m = \frac{h_{2}}{h_{1}} = \frac{v}{u}$ $m$ negative → real, inverted image; $m$ positive → virtual, erect image. $|m| > 1$ magnified; $|m| < 1$ diminished.

Table linking the signs of image distance and magnification to the nature of the image
Sign of v	Sign of m	Image
Positive	Negative	Real, inverted, other side of lens
Negative	Positive	Virtual, erect, same side as object

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