Simple microscope
A single convex lens of short focal length f, held close to the eye with the object inside f, gives an erect, virtual, magnified image.
- Image at the near point (D = 25 cm): m = 1 + D/f.
- Image at infinity (relaxed eye): m = D/f.
A lens of f = 5 cm gives m = 1 + 25/5 = 6 at the near point.
Compound microscope
It uses two convex lenses: an objective of very short focal length near the object and an eyepiece that acts as a simple microscope. The objective forms a real, inverted, magnified image, which the eyepiece magnifies further. Total magnification m = m_o × m_e. With the final image at infinity: m ≈ (L/f_o)(D/f_e) where L is the tube length (distance between the second focal point of the objective and the first focal point of the eyepiece). With L = 15 cm, f_o = 1 cm and f_e = 2.5 cm: m = 15 × 10 = 150.
Astronomical (refracting) telescope
It uses an objective of large focal length and large aperture (to collect more light and form a bright image of distant objects) and an eyepiece of short focal length. In normal adjustment, the final image is at infinity:
- Magnifying power m = f_o/f_e (often written with a minus sign to show the image is inverted).
- Length of tube = f_o + f_e.
With f_o = 100 cm and f_e = 5 cm: m = 20 and length = 105 cm.
Reflecting telescope
Large telescopes use a concave mirror as the objective (e.g. the Cassegrain design). Advantages: no chromatic aberration; a mirror can be supported over its whole back, so it can be made very large without sagging; a parabolic mirror removes spherical aberration; and a large mirror is easier to make than a large flawless lens.
Key points
- Simple microscope: m = 1 + D/f (near point), D/f (infinity).
- Compound microscope: m ≈ (L/f_o)(D/f_e).
- Telescope: m = f_o/f_e; length f_o + f_e.
- Telescope objective: large f and aperture; microscope objective: short f.
Common mistakes
- Swapping the roles of objective and eyepiece focal lengths between microscope and telescope.
- Forgetting the "1 +" for an image at the near point.