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what is linear magnification

Linear magnification is the ratio of the size (height or length) of an image to the size of the object, measured in directions perpendicular to the optical axis, and it shows how many times bigger or smaller the image is compared with the object.

What is linear magnification?

In optics, linear (also called lateral or transverse) magnification compares the linear size of the image and the object.

  • If m>1m>1m>1, the image is larger than the object.
  • If 0<m<10<m<10<m<1, the image is smaller.
  • If mmm is negative, the image is inverted (upside down) relative to the object.

In simple school physics for mirrors and lenses, linear magnification is usually defined as:

m=h′hm=\frac{h'}{h}m=hh′​

where h′h'h′ is the height of the image and hhh is the height of the object.

Formula and no-unit nature

For spherical mirrors and thin lenses, you often see both forms:

  • m=h′hm=\dfrac{h'}{h}m=hh′​ (image height ÷ object height)
  • m=−vum=-\dfrac{v}{u}m=−uv​ (image distance ÷ object distance, with sign convention)

Because magnification is a ratio of two lengths, it has no unit ; it is a pure number.

Quick example (story-style)

Imagine you place a 2 cm tall object in front of a lens, and the image formed on a screen is 6 cm tall.

  • Here, h=2h=2h=2 cm and h′=6h'=6h′=6 cm, so

m=62=3m=\frac{6}{2}=3m=26​=3

  • This means the image is three times taller than the object (a magnification of 3).

If instead the image height were −1-1−1 cm (negative sign indicating it is inverted), then

m=−12=−0.5m=\frac{-1}{2}=-0.5m=2−1​=−0.5

which means the image is half the size of the object and inverted.

Where it shows up in exams and discussions

Students most often meet “what is linear magnification” in:

  • Class 10 and 12 light/optics chapters (mirrors and lenses).
  • Questions that ask you to calculate image size or distance from given object size/distance.

You’ll also see it explained in short video lessons and forum-style homework help threads, which repeat the same key idea: it tells you how much bigger or smaller the image is compared to the object.

TL;DR:
Linear magnification mmm = image size ÷ object size, often written m=h′h=−vum=\dfrac{h'}{h}=-\dfrac{v}{u}m=hh′​=−uv​; it has no unit, and the sign tells you whether the image is upright or inverted.

Information gathered from public forums or data available on the internet and portrayed here.