Image 1 Caption: A plane reflection of a distorted brown oval through a plane to create a distorted green oval followed by a second plane reflection through a second plane parallel to the first one in order to create a distorted blue oval.

Features:

1. The net effect of the 2 plane reflections is a translation in this diagram.

2. Plane reflection---when you think about it while jumping up and down on one foot with hands on top of your head---gives an intrinsic a front-to-back inversion through the reflection plane. Another aspect of plane reflection is that it turns right-handed Cartesian coordinate systems into left-handed Cartesian coordinate systems.

3. Plane reflection is a mathematical concept that is physically realized in mirror reflection by mirrors---by which we mean plane mirrors if the term is NOT qualified somehow.

   The mirror surface is the reflection plane, of course.

4. In mirror reflection (for plane mirrors) the image is always a virtual image.

   To understand real image and virtual image in optics, let's consider real image formation and then virtual image formation:

   1. Real image formation:

      Consider a point source of light. Say in an optical device, a fraction of light rays from the point source converge to an image point, actually pass through it, and then diverge from that image point which is then seen in some directions as the image of the point source: in other directions there is nothing to be seen: the image is NOT a complete recreation of the point source. A continuum of point sources creates a finite source and a continuum of image points which creates a finite image: which can only be seen in certain directions.

      The image is called a real image since there is actual light at the image points and you can detect it for example with a camera.

   2. Virtual image formation:

      In virtual image formation, light rays from a source diverge from the image points, but do NOT actually start at those image points. Reflections and/or refractions in an optical device put the light rays on those divergent paths. Image 2 below shows an example of light rays being put on divergent paths from an image point.

      The image is called a virtual image since it has the effect of being a source of light rays, but there is NO light at the image points: there's nothing at them and you CANNOT take an image at them.

      As aforesaid, mirror reflections always give virtual images---the images exist in "mirror space." Mirror reflection is illustrated adjacently in the Image 2.

5. Image 2 Caption: The point source A emits light rays that reflect from the mirror obeying law of reflection. The mirror reflection creates the virtual image A' from which the reflected light rays diverge without ever having been at A'.

6. Mirror reflection is often used in optical devices because it does NOT the distort the image relative to the source other than the aforesaid front-to-back inversion of plane reflection.

7. The front-to-back inversion is the intrinsic inversion of mirror reflection and mirror inversion can always be understood in term of front-to-back inversion. For an illustration, see Image 3 below.

   

8. Image 3 Caption: "Mount Hood reflected in Mirror Lake (Clackamas County, Oregon), Oregon, USA." (Slightly edited.) The front-to-back inversion of mirror reflection is obvious in this orientiation of viewing.

9. But of what about the well-known mirror inversion that is usually noticed as a right-left inversion when you look at yourself in a mirror?

   Mirror inversion is, in fact, the combination of front-to-back inversion and the observer's orientation.

   The observer's orientation is important in looking at sources too. If you look at source and then stand on your stand on your head---which is NOT recommended---there's an inversion.

   For an example of mirror inversion, say you are facing a cross marked with cardinal directions: NESW going clockwise per usual. Behind you is a mirror. You can rotate your head to look at the cross image in different ways:

   1. You rotate your head around the vertical. The cross image has NWSE. There has been an inversion around the vertical. This is sometimes called flopped inversion.
   2. You rotate your head around the horizontal. The cross image has SENW. There has been an inversion around the horizontal. This is sometimes called flipped inversion.
   3. You rotate your head around a general direction. There is no inversion along that direction, just around the line perpendicular to it. This general inversion is just mirror inversion without qualification. One could also call this inversion a 2-d axis reflection about an axis which is the rotation axis of the observer projected onto the mirror.

   The upshot is that plane reflection (which gives the intrinsic front-to-back inversion through the reflection plane) plus the observer orientation results in mirror inversion.

Images:

1. Credit/Permission: © Pietro Battiston (AKA User:Toobaz, 2006 / Creative Commons CC BY-SA 3.0.
   Image link: Wikimedia Commons.
   
2. Credit/Permission: User:Fffred, 2006 / Public domain.
   Image link: Wikimedia Commons.
   
3. Credit/Permission: Oregon's Mt. Hood Territory, before or circa 2006 (uploaded to Wikimedia Commons by Howard Cheng (AKA User:Howcheng), 2006) / Public domain.
   Image link: Wikimedia Commons.