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).
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
- Draw the plane mirror as a straight vertical line and indicate the normal at the point where the incident ray meets the mirror.
- Place the object in front of the mirror (e.g., a short vertical arrow representing a ruler).
- Choose at least two points on the object (top and bottom). From each point draw an incident ray to the mirror.
- At the point of incidence draw the normal. Measure the angle of incidence \(i\) with a protractor.
- 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).
- Extend each reflected ray backwards behind the mirror as a dotted line. The extensions intersect at the image points.
- Join the image points to obtain the complete virtual image.
Characteristics of the Image Formed by a Plane Mirror
| Characteristic | Explanation (Cambridge syllabus) |
|---|---|
| Same size as the object | The 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 front | From the image‑distance rule, \(di = do\). If the object is 0.30 m in front, the image appears 0.30 m behind. |
| Upright | The reflected rays diverge in the same sense as the incident rays, so the image is not inverted. |
| Laterally inverted | Left–right (or front–back) orientation is reversed; text appears backwards. |
| Virtual | The 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.