The Mirror/Lens Sign Convention Map 🗺️

Do sign conventions for mirrors and lenses make your head spin? Let's turn your optical problems into a simple, visual map on a coordinate plane!

Subject: Physics • Classes: 10–12 • Difficulty: intermediate

The Trick

Imagine the spherical mirror's pole or the spherical lens's optical centre is the origin (0,0) of a standard Cartesian coordinate system. The principal axis is your X-axis. All distances are measured from this origin. Distances to the right are positive (+), to the left are negative (-). Heights measured upwards from the principal axis are positive (+), downwards are negative (-). Remember: The object is ALWAYS placed to the left of the mirror/lens.

Step-by-Step

  1. Step 1: Set Your Origin — Place the pole (for mirrors) or optical centre (for lenses) at the origin (0,0) of an imaginary Cartesian coordinate system. The principal axis is your X-axis.
  2. Step 2: Position the Object — Always place the object on the left side of the origin. This means the incident light rays travel from left to right. Therefore, object distance '$u$' is always negative.
  3. Step 3: Measure Horizontal Distances — Distances measured from the origin towards the right are positive (+). Distances measured from the origin towards the left are negative (-). This applies to image distance ($v$), focal length ($f$), and radius of curvature ($R$). (e.g., real image on right is +$v$, virtual image on left is -$v$). For concave mirrors/convex lenses, $f$ is negative/positive respectively.
  4. Step 4: Measure Vertical Heights — Heights measured upwards from the principal axis are positive (+) (e.g., object height $h_o$, erect image height $h_i$). Heights measured downwards from the principal axis are negative (-) (e.g., inverted image height $h_i$). A positive magnification ($m$) means an erect image, negative means inverted.

Frequently Asked Questions

Why is the object always placed on the left?
This is a universal convention to standardize the direction of incident light, which is always assumed to travel from left to right.
Does this work for both mirrors and lenses?
Yes, this Cartesian sign convention is universally applicable to both spherical mirrors and spherical lenses, making it a powerful tool.

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