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Lesson 15 · Magnification
How big — and which way up
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How big — and which way up

Magnification answers the honest question: how many times bigger is the image than the thing itself? As a ratio of heights, m=hihom = \dfrac{h_i}{h_o} — read aloud: m equals h-i over h-o. The subscripts are just the words: hih_i is the image height and hoh_o the object height, both in centimetres — the same i-for-image, o-for-object convention did_i and dod_o used last lesson. A ratio of two heights wears no units: m=3m = 3 means three times taller, m=0.5m = 0.5 means half size. The same number also hides in the distances from last lesson: m=−didom = -\dfrac{d_i}{d_o} — m equals minus d-i over d-o. Two roads, one answer.

About that minus sign — it is a message, not a mistake. When a lens throws a real image onto a screen, the image comes out upside down, and a negative mm is simply how the math reports it. m=−2m = -2 reads: twice as tall, inverted. So keep the sign when the distances hand it to you, and never be alarmed by it — the picture in a camera lands upside down too, and the camera simply flips it back for you.

mdodi

m=−didom = -\frac{d_i}{d_o}

  • mm= Magnification
  • did_i= Image distance (length)
  • dod_o= Object distance (length)
Lens Magnification (m = −d_i/d_o) solver →
hohim

m=hihom = \frac{h_i}{h_o}

  • mm= Magnification
  • hih_i= Image height (length)
  • hoh_o= Object height (length)
Magnification from Heights (m = h_i/h_o) solver →