# The Angle of Reflections

The reflection of a vertical object in a flat reflecting surface appears as a duplicate of the object's height. A post standing vertically in calm water will be approximately the same height in the perceived reflection as it is above the water.

If a post in the water is not vertical but leans toward the viewer, its reflection will be longer than the post itself appears. If the post leans away from the viewer, its reflection will be shorter than the post appears. These variations in reflection length exist because we are viewing the object from the vantage point of the reflecting surface.

When part of the outline of an object's silhouette is parallel to the picture plane (the paper's surface) and that outline contacts a reflecting surface, it is possible to calculate the correct angle of the object's reflection. The illustration at the bottom of the page shows how this works with cone-shaped objects.

Draw a line parallel io the reflecting surface where the edge of the object's silhouette meets that surface. (If the reflecting surface is level, the line is parallel to the horizon.) The angle from this line up to the edge of the object will be equal to the angle from the line down to the edge of the object's reflection. An object perpendicular to the surface that reflects it has its height duplicated in the reflecting surface. Because reflections are the view we get from the reflecting surface, we see more of an object's underside in its reflection than we do when looking at the object itself. This is why the reflection of a forward-tilting post is longer than the post itself appears. The posts seem to have dark reflections, which are actually not reflections per se but the absence, or blocking out, of the sky's reflection in the water. Except in mirrors and polished metal, there are no reflections darker than the reflecting surface. Reflections should not be confused with cast shadows. If the edge of an object's silhouette is parallel to the picture plane, we can calculate the angle of that edge in its reflection. Draw a line parallel to the reflecting surface where the object touches it. (If the surface is level, the line is parallel to the horizon.) The angle from this line to the edge of the object is equal to the angle from this line to the edge of the reflection.    