Re: Why can't you see shadows that well on a mirror?

Why don't you shadows in a mirror?  Consider the following situation: a
light bulb in the center of a room casts light.  You place a tennis ball
between the light bulb and a mirror on the wall.  The tennis ball casts a
shadow on the mirror.  Now, how are you going to look at the shadow?

Well, if you stand off to the side a bit (say, to the right), so that you
don't interfere with the tennis ball's shadow, then when you look at the
mirror, you are seeing light rays which have come from the _other_ side of
the tennis ball (from the left), bounced off the mirror, and reached your
eyes.  The light rays "in the shadow" travel straight from the tennis ball
to the mirror and bounce straight back to the tennis ball.  Because you are
standing off to the side, they don't reach your eyes.

So, suppose you stand directly behind the tennis ball, so that those light
rays "in the shadow" will bounce straight off the mirror to you.  Ooops --
now YOU are blocking all the light from the bulb which passes close to the
tennis ball.  If the light bulb is the only source in an otherwise dark
room, then you will see a silhouette of your head in the mirror.  You won't
be able to see your eyes and nose very well, because they are in the dark.
In effect, you are seeing a shadow (of yourself) in the mirror.

In order to see clearly the shadow of some other object in a mirror, you
can try the following: go into a dark room with a single light source. 
Stand off to the side of the light source, and place a mirror at an angle
so that it reflects the light from the source to you (i.e. so that you see
the light source in the mirror.  Now, have someone else hold a piece of
cardboard between the mirror and the light source.  The cardboard will
block the light rays from reaching the mirror -- casting a shadow on it. 
When you look at the mirror, it will be much darker than before -- you are
seeing the shadow of the cardboard.

In ordinary circumstances, we are used to seeing shadows as diffuse dark
patches on surfaces; people standing just about anywhere will be able to
see the dark patches and agree on their appearance.  This is a consequence
of the nature of most surfaces (like walls and floors): they are rough,
with little pits and grooves and hills that reflect light in all
directions.  Light falling on such a surface is reflected in all
directions, so people everywhere agree that the surface is bright.  When
light is blocked so that a shadow is cast on the surface, everyone can see
that the light from the wall is diminished, and they all say, "There's a
shadow."  

But a mirror is a very smooth surface, which reflects light only in one
direction.  Different people in different positions will NOT agree on the
brightness of a mirror, and they will NOT detect the presence of a shadow
equally.

You also ask about very dark surfaces: would shadows be invisible on them? 
Well, imagine a wall made of a material which reflects no light at all. 
Anyone who looks at the wall will see -- nothing.  No light.  It will be
perfectly black.  Shine a flashlight on the wall -- and you see nothing. 
Now block the flashlight's beam with a piece of cardboard.  Look at the
wall.  What do you see?  Nothing.  There's no difference, whether you block
the beam or not.  So, you don't notice a shadow.

No actual surface reflects absolutely zero light, so no actual surface will
do this.  But it is difficult to detect shadows cast on dark surfaces.