Compound microscope

The compound microscope is the reverse of the telescope: it is used to see very close objects. Here too there are two converging lenses, but with both focal lengths small: $f_\text{ob} \sim 1$–$10$ mm (objective in contact with the slide) and $f_\text{oc} \sim 10$–$30$ mm (eyepiece).

The object is placed just beyond the focus of the objective, which forms a real, magnified and inverted image on the front focal plane of the eyepiece. The eyepiece acts as a magnifying glass and sends the final virtual image to the eye.

Key formula

The total magnification is the product of the two magnifications: $\ev{G_\text{mic} = G_\text{ob}\cdot G_\text{oc} = \frac{L}{f_\text{ob}}\cdot\frac{d_0}{f_\text{oc}}}$ where $L$ is the distance between the two foci concerned (the mechanical length of the microscope, in practice $\sim 160$ mm in standard models) and $d_0 = 25$ cm is the distance of distinct vision.

Example — A school microscope

Typical school microscope: objective $f_\text{ob} = 8$ mm, eyepiece $f_\text{oc} = 25$ mm, $L = 160$ mm. What is the magnification?

$G_\text{ob} = L/f_\text{ob} = 160/8 = 20$; $G_\text{oc} = 250/25 = 10$; $G_\text{tot} = 20\cdot 10 = 200\times$. Onion plant cells, large bacteria and starch granules are within its reach.

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