Quill wants to predict where a lens will form its image, without a lab bench. The tool is a drawing. But a drawing needs rays whose paths after the lens are known in advance, and most rays' paths are not.
A few special rays have exit paths you can state before drawing anything. They are called principal rays, and this beam-drawing toolkit starts with the first: the ray that arrives parallel.
You already know what a lens does to a whole beam of parallel rays: a convex lens converges them at its focal point, and a concave lens spreads them from its virtual focal point.
The parallel-ray rule applies that knowledge to ONE ray at a time: a ray from the top of an object, arriving level.
Away from means this: draw the dashed line from the virtual focal point to the bending point; the ray leaves along that line's direction, continuing outward.
One rule, two cases, one read: parallel in, focal point out. The convex case passes THROUGH its focal point; the concave case points AWAY FROM its virtual focal point.
In the family's drawings the bend is drawn once, at the lens plane: thin-lens diagrams simplify the two surface bends into one.
This is rule 1 of the lens toolkit. Two more principal rays follow in the next lessons.
A ray from a candle flame travels parallel to the principal axis into a convex lens of focal length 10 cm. State its path after the lens.
The ray arrives parallel to the axis, so the parallel-ray rule applies.
Through a convex lens, the parallel ray bends to pass through the focal point on the far side.
That focal point sits 10 cm beyond the lens, on the axis.
After the lens, the ray travels through the focal point 10 cm beyond the glass and continues on.
The same flame's parallel ray now enters a concave lens of focal length 10 cm. State its path after the lens.
The ray arrives parallel to the axis, so the parallel-ray rule applies.
Through a concave lens, the ray bends directly away from the virtual focal point on the incoming side.
That point sits 10 cm in front of the lens; the exit path lies along the dashed line from that point through the bend, continuing outward.
After the lens, the ray spreads outward along the line traced from the virtual focal point, never crossing the axis.
A ray travels parallel to the principal axis into a convex lens. Where does it go after the lens?
A ray travels parallel to the principal axis into a concave lens. Which path does it take after the lens?
A ray from the BOTTOM of an object travels parallel to the principal axis, below the axis, into a convex lens. Where does it go after the lens?
Which statement is rule 1 of the lens toolkit, for a convex lens?
In a concave-lens drawing, a dashed line is drawn from a focal dot through the point where the parallel ray bends. Which dot is it?
After a lens, a drawn parallel ray angles outward, and its dashed extension passes through a dot on the incoming side. Which element is this?