Optical instruments: magnifier, microscope and telescope
PhysicsOpticsAges 14–15
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Ray diagrams of the magnifying glass (M = D/f relaxed, 1 + D/f at the near point), the compound microscope (real intermediate image, M ≈ (L/fₒ)(D/fₑ)) and the refracting or reflecting telescope (M = fₒ/fₑ in normal adjustment). The Rayleigh criterion θ = 1.22λ/D shows when two stars are resolved as the aperture and wavelength change, light-gathering power grows as D², an atmosphere chart shows which wavebands need space telescopes, and a spectroscope matches a star's dark lines with H, He, Na, Ca and Fe.
Lesson: Optical instruments; Magnifying glass; Microscope; Telescope; Resolving power
What it shows
Optical instruments make small or distant things look bigger by increasing the angle they subtend at the eye. A magnifying glass forms an upright virtual image; a compound microscope adds an objective that makes a real magnified image for the eyepiece; a telescope's objective lens or concave mirror makes an image of a distant object at its focal plane. A wider aperture collects more light (∝ D²) and gives finer detail, limited by diffraction (Rayleigh criterion). Thin lenses and paraxial rays are assumed; the atmosphere chart is a simplified average for a clear sky.
How to use
On Magnifier, change the focal length and the object distance, or press Relaxed eye or Image at 25 cm. On Microscope, set the objective, the eyepiece and the distance between the lenses, then press Normal adjustment. On Telescope, choose Refracting or Reflecting and change fₒ, fₑ and the aperture. On Resolving power, change the aperture, the wavelength and the separation until the stars are just resolved. On Atmosphere and spectra, pick a waveband, then a star, and tick elements to match its lines.
Parameters you can change
- Screen Magnifier, Microscope, Telescope, Resolving power, Atmosphere and spectra
- Magnifier focal length f 2.5–10 cm
- Magnifier object distance u 1–10 cm
- Microscope objective fₒ 0.4–2 cm
- Microscope eyepiece fₑ 2–8 cm
- Microscope distance between the lenses 12–25 cm
- Microscope object distance uₒ 0.41–3.2 cm
- Telescope type Refracting (lenses), Reflecting (mirror)
- Telescope objective fₒ 40–200 cm
- Telescope eyepiece fₑ 0.5–10 cm
- Eyepiece moved in/out Δ -1–0.5 cm
- Aperture D 0.5–1000 cm
- Wavelength λ 400–700 nm
- Separation of the stars θ 0.01–100 ″
- Star Star A (like the Sun), Star B (hot, blue-white), Star C (cool, orange)
- Waveband Gamma rays, X-rays, Ultraviolet, Visible light, Infrared, Microwaves, Radio waves
Questions to explore
- Why does a telescope with a longer objective focal length and a shorter eyepiece focal length give a larger angular magnification?
- How does doubling the aperture change the light collected and the smallest angle that can be resolved?
- Why must X-ray and ultraviolet telescopes be placed in orbit, while radio telescopes work on the ground?
