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Wize University Physics Textbook (Master) > Geometric Optics

Plane Mirrors

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Plane Mirrors



When an object is a distance dod_o from a plane mirror, the image is virtual and appears at a distance did_i behind the mirror , and we have:

 di=do \boxed{\ d_i=d_o \ }




The height of the object is the same as the height of the image: hi=hoh_i=h_o


Note: you might see different notations for the distances ( did_i and dod_o, ii and oo, pp and qq ).


Wize Concept
Images formed by a plane mirror are:
  • Virtual
  • Upright
  • Unmagnified
  • Left-right reversed
  • Front-back reversed



Wize Tip
  • Draw a straight line from the object going perpendicular to the mirror, and extend it on the other side. The ray on the other side will be dotted (imaginary).
  • Draw a line from the tip of the object going at an angle to the mirror, and reflect it at the same angle. Extrapolate the reflected ray behind the mirror as a dotted line.
  • Find the intersection point of the dotted rays behind the mirror. This point is the image point.

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Example: Two Twins


Two twins are standing 5.25.2 m in front of a mirror comparing outfits. They are 2.52.5 m from the mirror.

a) At what angle should one of the twins shine a laser so that the reflected beam hits the other twin? (in degrees)

b) Where is the image of the laser formed behind the mirror?

Part a)


Draw a diagram showing incident and reflected angles (equal to each other) and the dimensions given:



Pick the triangle with θi\theta_i or θf\theta_f in it.

The opposite side is half of the distance between the twins, 5.22=2.6\dfrac{5.2}{2}=2.6 m.
The adjacent side is the distance to the wall, 2.52.5 m

The angle is then:

tan⁡θi=2.62.5   →   θi=46°\tan\theta_i=\dfrac{2.6}{2.5}\ \ \ \to \ \ \ \theta_i =46\degree

Part b)


The image should appear to be at the same distance of 2.52.5 m behind the mirror.

Practice: Multiple Mirrors


A girl stands 22 m in front of a vertical plane mirror. Just 33 m behind her is a second vertical plane mirror. Determine the distance between her and the 5th5^{th} nearest image that can be seen in either mirror.