Optical Instruments: Microscope and Telescope

Identify the instrument; note whether final image is at near point or infinity; choose the correct magnifying power formula; substitute focal lengths in the same unit; interpret whether magnification is linear or angular depending on the instrument.

Microscope diagram should label object, objective, intermediate image, eyepiece and final virtual image. Telescope diagram should label distant object rays, objective, focal plane, eyepiece, tube length and final rays for normal adjustment.

A common wrong answer is using M = 1 + D/f for a telescope, which is a simple microscope formula and does not apply to distant-object angular magnification.

Optical instruments use lenses or mirrors to increase the apparent size or resolving usefulness of objects. A microscope magnifies nearby small objects, while a telescope increases the angular size of distant objects.

Optical instruments use lenses or mirrors to increase the apparent size or resolving usefulness of objects. A microscope magnifies nearby small objects, while a telescope increases the angular size of distant objects. Simple microscope magnifying power for final image at near point: M = 1 + D/f; for relaxed eye: M = D/f. Here D is least distance of distinct vision, usually 25 cm, and f is focal length of the convex lens in the same unit. Telescope in normal adjustment: M = f_o/f_e, where f_o is objective focal length and f_e is eyepiece focal length. These formulas assume thin lenses and small-angle viewing. A laboratory compound microscope uses a short focal length objective near the specimen and an eyepiece near the eye. An astronomical telescope uses a large focal length objective pointed at distant stars or planets.

A simple microscope is a convex lens used so that the final image is formed at the near point or at infinity. A compound microscope uses an objective of small focal length to form a real magnified intermediate image, which is further magnified by the eyepiece. A refracting telescope uses an objective of large focal length and aperture to form an image of a distant object, and an eyepiece to view it at a larger angle. The design goal differs: a microscope needs high magnification for nearby objects, while a telescope needs angular magnification and light-gathering ability for distant objects. Simple microscope magnifying power for final image at near point: M = 1 + D/f; for relaxed eye: M = D/f. Here D is least distance of distinct vision, usually 25 cm, and f is focal length of the convex lens in the same unit. Telescope in normal adjustment: M = f_o/f_e, where f_o is objective focal length and f_e is eyepiece focal length. These formulas assume thin lenses and small-angle viewing. A simple microscope has focal length f = 5 cm. Taking D = 25 cm, magnifying power for near-point viewing is M = 1 + D/f = 1 + 25/5 = 6. For relaxed viewing, M = D/f = 25/5 = 5. Near-point viewing gives greater magnification but is less comfortable for long observation. It appears in derivations of magnifying power, comparison of microscope and telescope lens choices, labelled ray diagrams, and numerical questions using D = 25 cm. A common wrong answer is using M = 1 + D/f for a telescope, which is a simple microscope formula and does not apply to distant-object angular magnification.