Jorun stands a tiny paper arrow 5 cm from a concave mirror whose focal length is 10 cm. The arrow now sits inside the focal length. Ray 1 still works. But the reflected rays never cross.
This lesson constructs the close-in case, where the reflected beams spread apart and the image must be traced, not caught.
The skeleton is the same as before, with one change: the arrow now stands between the mirror and the focal point.
Ray 1 leaves the tip parallel, and reflects through the focal point, exactly as before.
For the second ray, use the center ray: from the tip to the point where the principal axis meets the mirror, reflecting at an equal angle below the axis.
Follow the two reflected rays. They spread apart as they leave the mirror and never cross in front of it.
So trace each reflected ray straight back behind the mirror, drawing the traced lines dashed.
The dashed lines cross behind the mirror, on the tip's side of the axis, farther from the axis than the tip.
No light is behind the mirror, so no screen can catch this image. It is virtual, seen by looking into the mirror.
An arrow stands 4 cm from a concave mirror with a focal length of 9 cm. Plan the rays that locate the image of its tip.
Ray 1: from the tip, parallel to the principal axis; it reflects through the focal point.
Ray 2: from the tip to the point where the axis meets the mirror; it reflects at an equal angle below the axis.
The reflected rays spread apart, so trace both straight back behind the mirror with dashed lines.
The image of the tip sits where the dashed lines cross.
Two rays, both traced back: the tip's image is at the dashed crossing behind the mirror.
Katla finishes the diagram for an arrow 6 cm from a concave mirror with a focal length of 14 cm. The dashed trace-backs cross behind the mirror, above the axis. Describe the image she draws.
Only the dashed trace-backs cross, so the image is virtual.
The crossing sits above the axis, on the same side as the arrow's tip, so the image is right side up.
The crossing sits farther from the axis than the tip, so the image is drawn taller than the arrow.
A virtual, upright, enlarged image arrow behind the mirror, at the dashed crossing.
In the close-in case, the two reflected rays spread apart in front of the mirror. What is the next step of the construction?
The dashed trace-backs cross behind the mirror, above the axis. Where is the image of the arrow's tip drawn?
Katla says: 'When the reflected rays spread apart, the image is found by tracing them straight back behind the mirror.' Is Katla correct?
Ivor completes the diagram for an arrow 3 cm from a concave mirror with a focal length of 8 cm. Which description fits the correct finished diagram?
In the finished close-in diagram, the lines behind the mirror are dashed. What do the dashed lines show?
Lennart's paper star stands 2 cm from a concave mirror with a focal length of 7 cm. He completes the ray diagram. Which describes the drawn image?