Thin lenses

A thin lens is a piece of transparent glass bounded by two curved surfaces, which alters the direction of rays by exploiting refraction. The good news is that the same equation used for mirrors applies to lenses: only the sign convention for the focal length changes.

Key formula

$\ev{\dfrac{1}{p} + \dfrac{1}{q} = \dfrac{1}{f}} \qquad I = -\dfrac{q}{p}$ Converging lens (convex): $f > 0$. Diverging lens (concave): $f < 0$.

A converging lens makes parallel rays converge towards the focus; a diverging lens makes them diverge as if they came from the focus. Here too, the position of the image is constructed graphically using three privileged rays, of which two are enough.

Principle — Ray construction (converging lens)

• A ray parallel to the axis passes through the focus $F'$ after the lens.
• A ray passing through $F$ before the lens exits parallel to the axis.
• A ray passing through the centre of the lens continues straight.

Image construction with a converging lens: the three privileged rays meet where the image forms, here real and inverted.

Optical power

The optical power of a lens is $\mathcal{D} = 1/f$, measured in m$^{-1}$, that is in dioptres (D). A $+3$ D lens has $f = 1/3$ m $\approx 33$ cm. The shorter the focal length, the stronger the lens.

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