The reversibility of light principle for an optical instrument states that if you exchange the object and image places the geometrical construction used to draw the path of light rays will be the same. This principle has later been extended to all the light rays, even if they they do not undergo reflections or refractions (on a surface or optical instrument): light rays travel the same way (using the same path) forward and backward.

This principle comes from the symmetry of the equations that determines the position of the object and image. For a thin lens or for a spherical mirror one has

`1/x_1 +1/x_2 =1/f`

with corresponding sign conventions for `x_1, x_2, f` (object position, image position and focal length). Thus if one reverses the object with the image he only exchanges the values of `x_1` and `x_2` (keeping the sign conventions) between them, and he obtains the same final value for the unknown variable.

The principle of reversibility states that light will follow exactly the same path if its direction of travel is reversed.

Using Snell's Law,

sin i

sin r

= 1n2

sin r

sin i

= 2n1

It follows that

1n2=

1

2n1

http://schools.matter.org.uk/content/Refraction/reversibility.html