Simple microscope: m = 1 + D/f (image at D) or m = D/f (image at ∞). Compound: m = m_o×m_e, m_o = L/f_o, m_e = 1+D/f_e. Astronomical telescope: m = f_o/f_e (inverted). Galilean: m = f_o/|f_e| (erect). Resolving power: telescope RP = D/(1.22λ); microscope RP = 2n sin θ/λ. D = 25 cm (least distance of distinct vision).
Instrument calculators
Microscope, telescope, resolving power
| Instrument | Formula | Notes |
|---|---|---|
| Simple microscope | m = 1 + D/f or m = D/f | D = 25 cm (normal / image at ∞) |
| Compound microscope | m = m_o × m_e, m_o = L/f_o, m_e = 1 + D/f_e | L = tube length |
| Astronomical telescope | m = f_o / f_e | Image inverted |
| Galilean telescope | m = f_o / f_e | Erect image, diverging eyepiece |
| RP (telescope) | RP = D / (1.22 λ) | D = diameter of objective |
| RP (microscope) | RP = 2n sin θ / λ | NA = n sin θ (numerical aperture) |
About optical instruments
A simple microscope is a single convex lens: m = 1 + D/f when the image is at the least distance of distinct vision D (typically 25 cm), or m = D/f when the image is at infinity. A compound microscope has an objective and an eyepiece: total magnification m = m_o × m_e with m_o = L/f_o and m_e = 1 + D/f_e. An astronomical telescope uses two converging lenses: m = f_o/f_e (inverted image). A Galilean telescope uses a diverging eyepiece for an erect image with m = f_o/|f_e|. Resolving power of a telescope: RP = D/(1.22λ). For a microscope: RP = 2n sin θ/λ.