Sec 4 Physics Thin Converging Lenses notes

A thin converging lens bulges in the middle: light refracts toward the thicker part at both surfaces, so rays entering parallel to the principal axis (the line through the centre at right angles to the lens) are steered inward and cross at one point — the principal focus, F. The distance from the optical centre (the middle of the lens) to F is the focal length f. A lens with a short focal length bends rays more sharply: focal length measures lens power in reverse.

Because light paths are reversible, a ray passing through F on its way to the lens emerges parallel to the axis on the far side. And any ray through the optical centre meets both surfaces head-on at the same slant, so it passes undeviated. These are the only three rays you ever need; every lens diagram is drawn with them.

To locate an image: draw the object as an upright arrow, then trace two construction rays from its tip — (1) parallel to the axis, refracting through F on the far side; (2) straight through the optical centre; (optionally (3) through the near-side F, emerging parallel). Where the refracted rays actually cross, the image of the tip is real; where they only appear to come from (trace them backwards with dotted lines), it is virtual. Draw to a stated scale — "1 cm : 5 cm" — and examiners award construction marks for neat, ruled lines.

Notice the pattern: as the object slides toward the lens (still beyond f), the real image retreats away and grows. At u = f the escaping rays are parallel and refuse to meet — no image on any screen. Push the object inside f and the crossing collapses to the same side as the object: the rays diverge, your eye back-tracks them, and an enlarged upright virtual image floats up. Real on the far side, virtual on the near side.

Linear magnification is defined as m = image height ÷ object height. Because a scale ray diagram fixes both image position and size, the same ratio can be written from distances: m = image distance ÷ object distance = v ÷ u. The two forms must agree — use one to compute and the other to check. Magnification is a ratio with no unit; heights must share the same unit before dividing.

m < 1 means diminished (camera), m = 1 same size (photocopier at 1:1), m > 1 magnified (projector, magnifier). Watch the classic slip: a projector claims m = 30 when a 35 mm slide paints a 105 cm picture — convert 105 cm to 1050 mm first, then divide.

Hold a stamp closer to a lens than its focal length and the refracted rays still spread apart as they leave. Your eye traces them backwards to a point behind the stamp: an enlarged, upright image you can see but can never catch on paper — virtual. Because the image subtends a larger angle at your eye than the object alone would, it looks bigger: that angular enlargement is all a magnifier needs.

Practical habits: bring the object just inside F for the largest clear view (at u = f exactly, the image retreats to infinity and nothing focuses); move the lens, not the stamp; and remember the image stays on the same side as the object — a favourite exam trap.

Hold a card where the image should be. A real image prints itself on the card, because light rays actually pass through that point — camera sensors, projector screens, retinas all exploit this. A virtual image leaves the card dark: the rays never meet there; they only appear to come from it (plane-mirror images, magnifier images). This one screen test classifies every image in ray optics, and quoting it earns explanation marks.

The vocabulary must be exact: real images formed by a single converging lens are always inverted; virtual images from a single lens are always upright. Answering "real and upright" for a lens is a contradiction — if your diagram says that, re-draw before moving on.