Quill stands a small lit arrow lamp 30 cm from a convex lens of focal length 10 cm, then slides a white card along behind the lens. At one spot, a sharp arrow appears on the card, upside down.
A drawing can predict that spot before the card ever moves: trace two rays of the lamp's beam through the lens. This is the first lens construction, and it uses two of the toolkit's rays.
Start with the skeleton: the lens, both focal dots 10 cm out, and the object arrow standing upright 30 cm from the lens.
The object sits beyond the focal point. That position is the case this lesson constructs.
From the arrow's tip, draw ray 1, arriving parallel to the principal axis: it bends at the lens and exits through the far focal point.
From the same tip, draw ray 2, through the exact center: it continues straight through.
The two refracted rays cross on the far side of the lens, below the axis.
The arrow's base sits on the axis, and its image sits on the axis too, so draw the image arrow from the axis down to the crossing: the image is upside down.
The rays actually meet there, so the image is real: a card at the crossing catches the sharp arrow. That is where Quill's card stopped.
The two drawn rays are the easy ones, not the only ones. Light from the tip passes through every part of the lens, and the lens converges all of it at the same image point.
So covering half the lens does not cut the image in half: the whole image still forms, dimmer, because less light gets through.
Run the construction for Quill's arrow: 30 cm from a convex lens, focal length 10 cm. State each step and read the image.
Draw the skeleton: lens, principal axis, focal dots at 10 cm each side, the arrow upright at 30 cm.
Ray 1 from the tip arrives parallel and exits through the far focal dot.
Ray 2 from the tip runs straight through the exact center.
The two refracted rays cross on the far side, below the axis.
Draw the image arrow from the axis to the crossing: it points downward.
The image is real and inverted, on the far side of the lens, where the card catches it.
Romilly checks the finished drawing with the toolkit's third ray, from the tip through the near focal point. Where should it go?
Rule 3: through the near focal point in, parallel out.
Every ray from the tip must pass through the tip's image point.
So the checking ray should exit the lens parallel to the axis and pass through the same crossing.
The third ray exits parallel and threads the same image point: the construction checks out.
In the construction, the two refracted rays from the arrow's tip cross below the axis on the far side of the lens. Where is the image of the tip?
Romilly says: 'Any two of the toolkit's rays from the tip are enough to locate the image point; a third ray only confirms it.' Is Romilly correct?
Thora covers the top half of the lens with a card while the arrow's image shows on the screen. She says half of the image will disappear. Is Thora correct?
An arrow stands 25 cm from a convex lens of focal length 10 cm. In the construction, the refracted rays from its tip cross below the axis on the far side. Which description of the image is correct?
Which sketch correctly locates the image of an arrow's tip through a convex lens, with the arrow beyond the focal point?
A white card is placed exactly at the crossing of the refracted rays, and a sharp arrow appears on it. Why does the card catch the picture?