Define and use the terms focal length, principal axis and principal focus (focal point)

Key Terms

• Principal Axis – the straight line that runs through the centre of the lens and is perpendicular to its surfaces. Think of it as the “spine” of the lens.
• Focal Length ($f$) – the distance from the lens to the point where parallel rays of light converge (or appear to diverge from). It tells you how strong the lens is.
• Principal Focus (Focal Point) – the actual point on the principal axis where the rays meet. There are two: one on each side of the lens.

Analogy: The Lens as a Sun‑Collector

Imagine a magnifying glass held over a sunny day. The glass bends the sunlight so that all the rays meet at a single spot – that spot is the principal focus. The distance from the glass to that spot is the focal length. The straight line that the glass sits on is the principal axis. Just like the magnifying glass, a thin lens can make a picture appear larger or smaller depending on how you place it relative to the object and the screen. 🌞🔭

Lens Formula (Thin Lens Equation)

Symbol	Meaning
$f$	Focal length of the lens
$u$	Object distance (positive if on the same side as incoming light)
$v$	Image distance (positive if on the opposite side of the lens)

The relationship between these distances is given by:

Use this equation to find any one of the three values if the other two are known. 📐

Exam Tips

• Always keep track of the sign convention: $u$ and $v$ are positive when measured in the direction of the light ray.
• Remember that a converging lens (positive $f$) brings parallel rays to a real focus; a diverging lens (negative $f$) makes them appear to diverge from a virtual focus.
• When the object is at the focal point ($u = f$), the image is at infinity ($v \to \infty$). This is the basis of a telescope’s objective lens.
• Use a diagram: sketch the principal axis, mark the lens centre, and indicate $u$, $v$, and $f$. Even a quick sketch helps you keep the geometry straight.
• Check units: all distances should be in the same units (usually centimetres).

Quick Practice Problem

A converging lens has a focal length of $f = 20\,\text{cm}$. An object is placed $u = 30\,\text{cm}$ from the lens. What is the image distance $v$ and is the image real or virtual? 📏

Solution: Use the thin lens equation:

Solve for $v$:


Thus $v = 60\,\text{cm}$. Since $v$ is positive, the image is on the opposite side of the lens – a real, inverted image. ??