Magnification Calculator

M = -d_i/d_o = h_i/h_o. Linear magnification of a lens or mirror.

Inputs

Result

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General calculation reads

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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Pick distance or heights.
  • Enter values.
  • Read M with sign.

About this calculator

Linear magnification = ratio of image size to object size, with sign indicating orientation. M = h_i / h_o = -d_i / d_o. |M| > 1 enlarged; < 1 reduced. Sign +: upright (virtual image); −: inverted (real image). Microscope: M = 100-1000+. Camera capturing distant object: M ≈ f / d_o (very small fraction). Magnifying glass: M = 1 + d_n/f where d_n is near-point distance ~25cm.

Frequently asked

Why negative for real images?+
Real images form on opposite side of object — inverted. Sign convention encodes this.
Microscope magnification?+
Total = objective × eyepiece. 10× objective × 10× eyepiece = 100×. High-end labs reach 1500-2000×.
Camera "zoom"?+
"Optical zoom" is focal-length range / smallest. 24-70mm lens = ~3× zoom. Doesn't directly map to M without scene distance.
Magnifying glass?+
M = 1 + d/f where d ≈ 25cm (least eye distance). 5cm focal length: M ≈ 6×.
Telescope?+
M = focal length objective / focal length eyepiece. 1000mm telescope + 10mm eyepiece = 100×.

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