region of the tiles between the pixels that are not straddling a gap two rays are shown emanating from the lower surface of the gap a and extending upwardly at an angle u03b8 c called the critical angle at the critical angle a ray is refracted to an angle parallel to the top surface of each layer 10 or 12 light reaching the surface with angles less than the critical angle exits the layers 10 and 12 and light reaching the surface with angles larger than the critical angle is totally internally reflected because of the critical angle light emitted from a point within the layers 10 and 12 can escape from the panels by traveling at most a lateral distance of d c which is equal to the thickness of the layers 10 or 12 times the tangent of the critical angle therefore light from any part of the gap a can be completely blocked by putting a black strip 14 of width w m equal to 2d c over the gap a because of the symmetry of the relevant optics this same black strip 14 also blocks any external rays not shown from detecting the gap a if the strip 14 width is less than 2d c but wider than the width of the top of the gap a then it will completely hide the top of the gap a and a portion of a gap region near the top of the gap a thus the strip 14 makes the top of the gap a and part or all of the underlying gap region invisible to a user in practice the black strip 14 may be slightly wider to account for any finite width of the gap a and for any.