Four devices, one formula

The same conjugate points equation governs lenses and mirrors of both types, with different sign conventions for the focal length. A single table summarises all four cases, worth keeping always at hand.

	Conv. lens	Div. lens	Concave mirror	Convex mirror
Sign of $f$	$f > 0$	$f < 0$	$f = +R/2$	$f = -R/2$
Real image possible?	yes if $p > f$	no	yes if $p > f$	no
Where $q > 0$ lies	behind the lens	—	in front of the mirror	—
Where the virtual image lies	in front of the lens	in front of the lens	behind the mirror	behind the mirror

In all four cases the same “passe-partout formula” holds:

Key formula

$\dfrac{1}{p} + \dfrac{1}{q} = \dfrac{1}{f} \qquad I = -\dfrac{q}{p}$

Just remember the sign of $f$ and the meaning of the signs of $p$ and $q$. Passe-partout, as Giancarlo says: a key that opens every door of geometric optics.

Collegamenti

Argomenti: Ottica Concetti: Lenti e specchi

Esercizi collegati: Problema — Raggi per oggetto oltre 2f (lente) · Problema — Raggi per specchio concavo con p minore di f · Esercizio svolto — Specchio concavo