If a black colored body absorbs all colors, why does the spectrum of light appear on a black shoe? Few days back in a 10 grade school practical, we were shown the dispersion of light by a prism to create spectrum. 
Then we went into the open sun and performed it under a linear building roof and same results were obtained.
But when a teacher took it in the light and the spectrum was displayed on the ground cement, a child's shoe can in the spectrum's way and the spectrum was still visible on his black shoe. 
Now my question is if the objects that appear black absorb the colors and radiate them back. 
So why does the spectrum appears on the shoe when the colors should be absorbed by the shoe material and no color but black must appear as it is the absence of any color radiated? 
And also i want to ask that do blackbodies radiate back the same color the absorb?
 A: Black object "absorb the light falling on them". Sure. But how much of the light is actually absorbed?
Your visual system works mostly on difference between stimulii, so "black" is usually incontrast to things that are less black. This is the origin of the Chubb illusion and the Checker shadow illusion.
Even very black day-to-day materials reflect some light. For instance copy tonor reflects a couple of percent of light.
Your classmates "black" shoe absorbs enough light that it is darker than everything you look at most of the time, but it does not absorb all the light, and in a dim space your eye is sensitive enough to see the small amount of reflected light.
A: Assuming his shoe wasn't completely black (i.e. darker than a sunless cave) then in general some light is reflected.  For example, if you can discern the texture of the fabric, then the shoe was not completely black and you can always expect to see some light reflected, although certainly not as much as light is reflected as from a white piece of paper.  Since a colored light from the prism was shining on his shoe, this is the light that you are partially seeing reflected.  Indeed, some or perhaps most of that prism light was likely absorbed by the shoe, but the portion that was reflected was the excess colored light that was not absorbed.
