Quill swaps the convex lens for a concave one and stands the lit arrow lamp 20 cm away. Through the glass the arrow looks small and right-way-up, and no card behind the lens finds any picture.
The concave lens gets its own construction, and its toolkit is shorter: the beam's fate is fixed by rule 1 and rule 2 alone.
Start with the skeleton: the concave lens, both focal dots 10 cm out, and the arrow standing upright 20 cm from the lens.
From the arrow's tip, draw ray 1, arriving parallel: at the lens it bends OUTWARD, directly away from the virtual focal point on the arrow's side.
Dash ray 1's trace-back: the dashed line runs from the bend point back through that near-side dot.
From the same tip, draw ray 2, through the exact center: it continues straight through.
After the lens the two refracted rays spread apart; they never cross on the far side.
That crossing sits between the lens and the near focal dot: closer to the lens than the arrow, and lower than the arrow's tip.
Draw the image arrow upright from the principal axis to that crossing: smaller than the object, on the object's side.
Ray 2's own path happens to pass through the meeting, but ray 1 arrives there only as a dashed trace-back. The rays from the tip never actually meet, so the image is virtual.
The third toolkit ray is not used: rule 3 is stated for convex lenses, and this construction never needs it.
Run the construction for Quill's arrow: 20 cm from a concave lens of focal length 10 cm. State each step and read the image.
Draw the skeleton: concave lens, principal axis, focal dots at 10 cm, the arrow upright at 20 cm.
Ray 1 from the tip arrives parallel and bends outward, its dashed trace-back running through the near-side dot.
Ray 2 from the tip runs straight through the exact center.
The refracted rays spread, so find where ray 1's dashed trace-back crosses ray 2's path: on the arrow's side, between the lens and the near dot.
Draw the image arrow there: upright, smaller than the object, closer to the lens.
The image is virtual, upright, and reduced, on the arrow's side of the lens.
Romilly repeats the construction with the arrow moved out to 40 cm from the same lens. Where does the image end up, roughly?
The same two rays apply: parallel-outward with its dashed trace-back, and straight through the center.
The trace-back still crosses the center ray on the arrow's side, between the lens and the near focal dot.
The crossing sits lower than before: the farther arrow makes a smaller image, still upright, still closer to the lens than the arrow.
Still on the arrow's side, between the lens and the focal dot: virtual, upright, and reduced.
Which two toolkit rays does the concave-lens construction use?
In the concave-lens construction, where does the image of the arrow's tip sit?
Thora says: 'In this construction, only one of the two refracted rays needs a dashed trace-back.' Is Thora correct?
An arrow stands 15 cm from a concave lens of focal length 5 cm. After the construction, which description of the image is correct?
Which sketch correctly constructs a concave lens's image?
A card is held exactly where the concave lens's construction puts the image. The card shows no picture of the arrow. Why?