Image Formation by Plane Mirrors

When you stand in front of a bathroom mirror, you see yourself — but where exactly is that 'you'? The image appears to be sitting behind the glass, at the same distance as you are in front of it. This is the fundamental behaviour of a plane mirror: a perfectly flat, smooth reflective surface. Understanding how plane mirrors form images is one of the most elegant applications of the law of reflection, and it underpins everything from periscopes to rear-view mirrors in cars. A plane mirror does not actually collect or focus light — it simply redirects rays according to the law of reflection (angle of incidence equals angle of reflection). When diverging rays from a point on an object strike the mirror and reflect, they continue to diverge on your side of the mirror. However, your brain assumes light travels in straight lines, so it traces those reflected rays backwards into the mirror. They appear to converge at a point behind the mirror — and that is where the image seems to be. Because no light actually passes through that point, it is called a virtual image. Four key characteristics define every image formed by a plane mirror: it is virtual (light only appears to come from it), erect (upright, the same way up as the object), the same size as the object (magnification = 1), and located as far behind the mirror as the object is in front of it. It is also laterally inverted — left and right are swapped, which is why text appears reversed in a mirror.

Key takeaways
  • The Law of Reflection in Action
  • Ray Tracing to Locate the Image
  • Object Distance Equals Image Distance
  • Lateral Inversion Explained
  • Magnification is Always Unity

The Law of Reflection in Action

Every point on the mirror obeys the law of reflection: the angle of incidence (measured from the normal to the surface) equals the angle of reflection. For a plane mirror, the normal at every point is perpendicular to the flat surface. This uniformity means parallel rays hitting different parts of the mirror reflect in a perfectly ordered way — there is no focusing or distorting of the beam as there would be with a curved mirror.

Ray Tracing to Locate the Image

To find where the image of a point object forms, draw at least two rays from the object to the mirror surface. Apply the law of reflection to find each reflected ray. These reflected rays diverge — they spread apart rather than meeting. Extend them backwards (as dotted lines) behind the mirror. The point where the backwards extensions meet is the image location. Since real light does not pass through this point (it is behind the mirror), the image is virtual.

Object Distance Equals Image Distance

By geometry, the image point is always located on the perpendicular from the object to the mirror, at an equal distance behind it. If your nose is 30 cm in front of the mirror, your nose's image is 30 cm behind it. Mathematically: image distance (v) = object distance (u), with the sign convention that v is negative when the image is behind a mirror (virtual). This can be stated as |v| = |u|.

Lateral Inversion Explained

Lateral inversion means left and right appear swapped. Imagine holding a transparent sheet of writing up to a mirror — the letters look backwards. Crucially, the mirror does not swap up/down, only the axis perpendicular to the mirror surface is reversed (depth is flipped). So a right hand held up appears as a left hand in the mirror. This happens because the image is formed by reversing the front-to-back dimension of the object, which our brain interprets as a left–right flip.

Magnification is Always Unity

The linear magnification m of a plane mirror is always exactly 1. The image height equals the object height, and the image width equals the object width. Nothing is stretched or compressed. This is why plane mirrors are used whenever an undistorted view is needed — unlike concave or convex mirrors which produce magnified or diminished images, a plane mirror reproduces the object faithfully in size, just shifted in apparent position to behind the surface.

The Key Equation

v=−uandm=hiho=1v = -u \quad \text{and} \quad m = \frac{h_i}{h_o} = 1
  • v — Image distance (metres (m) or centimetres (cm)): Distance from the mirror to the image. Negative by sign convention when the image is virtual (behind the mirror).
  • u — Object distance (metres (m) or centimetres (cm)): Distance from the mirror to the object. Taken as positive when the object is in front of the mirror (real object).
  • m — Linear magnification (dimensionless): Ratio of image height to object height. For a plane mirror this is always +1, indicating an erect, same-size image.
  • h_i — Image height (metres (m)): The measured height of the image formed by the mirror.
  • h_o — Object height (metres (m)): The measured height of the original object.

Worked Example

Problem. A student stands 1.8 m in front of a large plane mirror. (a) How far behind the mirror does their image appear? (b) If the student is 1.65 m tall, what is the height of their image? (c) The student walks 0.6 m towards the mirror. How far apart are the student and their image now?

∣v∣=1.8 m,hi=1.65 m,dtotal=2.4 m|v| = 1.8\,\text{m},\quad h_i = 1.65\,\text{m},\quad d_{\text{total}} = 2.4\,\text{m}

Answer. The image forms 1.8 m behind the mirror, is 1.65 m tall, and after moving closer the student and image are 2.4 m apart.

Figure
Diagram
MirrorObject (O)Image (I)normalu (object dist.)v = u (image dist.)Reflected rays (solid)extended back (dashed) → virtual imageIncident rays from object
Origins · 1 minHero of Alexandria and how this was discovered
HO
Hero of Alexandria
10–70 · Greek (Egyptian)

Hero of Alexandria was among the first to formulate the law of reflection rigorously, stating in his work 'Catoptrica' that light travels by the shortest path — which leads directly to the equal-angles reflection rule. His analysis of mirrors, including flat (plane) mirrors, laid the geometric foundation that all later optics, including image formation theory, is built upon. Hero also invented an early steam-powered device called the aeolipile, described a rudimentary vending machine, and designed automatic theatre doors — making him arguably the world's first mechanical engineer, not just an optics pioneer.

  • Law of Reflection — Image formation by a plane mirror is a direct consequence of the law of reflection; understanding angle of incidence equals angle of reflection is essential before analysing mirror images.
  • Image Formation by Concave Mirrors — Concave mirrors also form images by reflection but can produce real, inverted, or magnified images — contrasting sharply with the virtual, erect, same-size images of plane mirrors.
  • Refraction of Light — Refraction is the other major way light changes direction and forms images, as in lenses; comparing reflection and refraction deepens understanding of how optical instruments work.
  • Spherical Mirrors and the Mirror Equation — The mirror equation generalises image-distance relationships to curved mirrors; the plane mirror result v = −u is the special limiting case when focal length approaches infinity.