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Czech River Rays

Jaroslav Fous caught this enchanting morning scene of sun rays breaking through trees and shining on a smooth river surface.

Some rays are reflected back upwards from the water, there are also mirror images.

But which are which? Why are their angles not what you would expect?

Image ©Jaroslav Fous, shown with permission
The apparent scene

Rays & mirror
image formation

The scene has downward sun rays formed by gaps in trees and upward rays reflected from the river surface.

Both are corporeal, they exist in real space, they can be touched, walked around, they show perspective effects.

As a complication the surface forms virtual mirror images of all these!

The ‘real’ reflected rays are hard to separate from the mirror images and they have shallower slopes. Surely a mirror should produce rays with the same slopes as the incident rays? “The angles of incidence and reflection are the same” – we are told.

There is no violation of reflection laws. The apparent contradiction arises from our expectation that reflections in a mirror look the same (except for being flipped) as the real object.

They do not.

Rays & Sticks

Instead of sun rays imagine several parallel but sloping sticks in the river. The sticks behave the same as rays.

To the eye above the water (mirror) surface the stick subtends a large angle 'A'. The stick reflection is another matter. In the eye position as shown the reflection subtends a much smaller angle 'B'. A shift in position can make the reflection disappear.

Now tilt the sticks sideways and their reflections look like those in the picture.

Bring the eye close enough and the parallel sticks appear to converge towards a 'vanishing point' as do the sun's rays.

This 3D geometry is hard to draw and describe. Do an experiment. Hold a pencil at an angle on a horizontal mirror. Get your eye close and see how the pencil's reflection behaves.