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The slides to the left illustrate how light is reflected radially off a cylinder. If the cylinder is vertical, then the view is from the top and the light is being sprayed out horizontally. Note that the intensity of the reflection is different from different viewing angles, but a reflection will be seen over a wide range of angles.


The drawing to the left shows how the vertical components of incoming rays are reflected.  Incident rays from the sun are yellow.  Reflected rays are blue. The incident rays are all in a plane as are the reflected rays but not necessarily the same plane.  The right edge of the visible cylinder is on a vertical line running the length of the cylinder.  Rays are reflected along this line as if a thin, flat mirror were placed tangent to that line as the surface normals along that line are all parallel (and horizontal).  Note that even though a reflection is present over the entire cylinder, an observer will see a reflection on only  a part of it.  Observers at positions 1 and 2 will see the reflection from the same place but observers at 3 and 4 will see it in higher positions.  The roles of horizontal and vertical are reversed for a horizontal cylinder.  With a little math, reflection is linear so the incident vector can be broken into vertical and horizontal components, each component reflected, and the results added to give the reflected vector.  Except for the top and bottom, all surface normals on the cylinder are horizontal.  The vertical component is perpendicular to the surface normal so it is unchanged by the reflection,  The horizontal component is by definition horizontal and the surface normals are horizontal so the reflection of the horizontal component is also horizontal.  The vertical part of the incident ray contributes only to the vertical part of the reflected ray and the horizontal part of the incident contributes only the horizontal part of the reflected ray.   As shown above, the horizontal component gets spread out horizontally, but the vertical components does not.  The reflection is then like a skirt whose thickness measured vertically is the height of the cylinder and which is all going down (assuming the sun was above) at the same angle as the incident rays.


For a rather crude demonstration of specular reflections from a real cylinder, click on the image to the left (17MB wmv file).  The cylinder was meant to be part of a face towel rack.  I first walk around the cylinder testing its reflection's sensitivity to horizontal movement.  If I had moved in a perfect circle around the cylinder then the reflection would not have moved up and down but I didn't and it did.  The point is that the reflection is not very sensitive to horizontal position.  Then I move up and down and the reflection follows me very closely showing that the reflection is very sensitive to vertical position.  I don't have to move up or down very far to make that reflection move completely off the cylinder.  The reflection is visible only in a narrow vertical band around the cylinder.