Describe the formation of an optical image by a plane mirror and give its characteristics, i.e. same size, same distance from mirror, virtual

3.2.1 Reflection of Light

Objective

To describe how a plane mirror forms an optical image and to state the image’s characteristics – same size as the object, same distance behind the mirror as the object is in front, upright, laterally inverted and virtual.

Key Definitions

  • Normal: a line drawn perpendicular to the reflecting surface at the point of incidence.

  • Angle of incidence (i): the angle between the incident ray and the normal.

  • Angle of reflection (r): the angle between the reflected ray and the normal.

Law of Reflection

The angle of incidence equals the angle of reflection:

\( i = r \)

Both angles are measured with respect to the normal (see diagram below).

Diagram showing incident ray, normal and reflected ray with i = r

Image‑Distance Rule for a Plane Mirror

For a plane mirror the object distance (\(do\)) and the image distance (\(di\)) are equal in magnitude but lie on opposite sides of the mirror:

\( di = do \)

Both distances are measured perpendicular to the mirror surface.

Step‑by‑Step Construction of the Image

  1. Draw the plane mirror as a straight vertical line and indicate the normal at the point where the incident ray meets the mirror.

  2. Place the object in front of the mirror (e.g., a short vertical arrow representing a ruler).

  3. Choose at least two points on the object (top and bottom). From each point draw an incident ray to the mirror.

  4. At the point of incidence draw the normal. Measure the angle of incidence \(i\) with a protractor.

  5. From the normal, draw the reflected ray on the opposite side such that the angle of reflection \(r\) equals the measured \(i\) (law of reflection).

  6. Extend each reflected ray backwards behind the mirror as a dotted line. The extensions intersect at the image points.

  7. Join the image points to obtain the complete virtual image.

Characteristics of the Image Formed by a Plane Mirror

CharacteristicExplanation (Cambridge syllabus)
Same size as the objectThe angles between any two incident rays are preserved on reflection, giving a magnification \(m = \dfrac{hi}{ho}=1\).
Same distance behind the mirror as the object is in frontFrom the image‑distance rule, \(di = do\). If the object is 0.30 m in front, the image appears 0.30 m behind.
UprightThe reflected rays diverge in the same sense as the incident rays, so the image is not inverted.
Laterally invertedLeft–right (or front–back) orientation is reversed; text appears backwards.
VirtualThe reflected rays actually diverge; they never meet. The brain extrapolates them back behind the mirror, so the image cannot be projected on a screen.

Worked Example (Typical IGCSE Exam Question)

Question: An object is placed 0.25 m in front of a plane mirror. State the position, size, orientation and nature of the image formed.

Solution:

  • Position: The image is 0.25 m behind the mirror (because \(di = do\)).

  • Size: The image is the same size as the object (magnification = 1).

  • Orientation: The image is upright but laterally inverted.

  • Nature: The image is virtual; it cannot be caught on a screen.

Summary Checklist

  • Normal → perpendicular to the mirror at the point of incidence.

  • Law of reflection: \(i = r\).

  • Image distance rule: \(di = do\).

  • Image characteristics – same size, same distance, upright, laterally inverted, virtual.

  • Construction: draw incident rays, apply the law of reflection, extend reflected rays behind the mirror to locate the virtual image.