Problem: Rays for a concave mirror with p less than f

Problem

Draw the ray diagram for a real object placed between the focus and the vertex of a concave mirror ($p < f$). Graphically locate the image and classify it (real or virtual, upright or inverted).

Solution

Graphical construction. From the tip of the object we draw:

• the ray parallel to the axis, which reflects passing through the focus $F$;
• the ray that hits the vertex $V$, which reflects symmetrically about the axis.

With $p<f$ the two reflected rays diverge: they do not meet in front of the mirror. Extending them behind the mirror (dashed lines) they intersect, giving a virtual image.

Classification.

$\ev{\text{virtual image, upright, magnified, behind the mirror}}$

This is the principle of the make-up / shaving mirror: bringing the face closer than the focus shows one’s own image magnified and upright.

Collegamenti

Argomenti: Optics Concetti: Lenses and Mirrors Competenze: Limiting-Case and Sci-Fi Physics Analysis