Optical instruments

Optical instruments make things look bigger by making them fill a bigger angle at the eye. Their magnifying power M is the ratio of angles: angle with the instrument ÷ angle with the naked eye (object placed at D = 25 cm, the near point, or far away for a telescope).

Magnifying power (an angle ratio) and magnification (an image size ratio, v/u) are different ideas, though sometimes equal.

Simple microscope (a convex lens used as a magnifier), focal length f:

• Image at the near point D: m = 1 + D/f.
• Image at infinity (relaxed eye): m = D/f.

A lens of f = 5 cm gives 6 or 5. Shorter f, stronger magnifier.

Compound microscope: two convex lenses. The objective (very short f) makes a real, enlarged image; the eyepiece magnifies that image further.

M = m_o × m_e, with m_o ≈ L/f_o (L = tube length) and m_e = D/f_e (or 1 + D/f_e). Example: m_o = 10 and an eyepiece of f_e = 5 cm (image at infinity, m_e = 5): M = 50. Both lenses should have short focal lengths.

Astronomical telescope: a long focal length objective and a short focal length eyepiece. In normal adjustment (final image at infinity):

M = f_o / f_e, and the tube length is f_o + f_e.

Example: f_o = 100 cm and f_e = 5 cm give M = 20 in a tube 105 cm long. With the image at D instead, M = (f_o/f_e)(1 + f_e/D), a little more.

A telescope's objective should also be wide, to gather more light and see fainter, sharper detail. Big modern telescopes use a curved mirror as the objective (reflecting telescopes): mirrors give no colour fringes and are easier to support than huge lenses.