Final answer:
In optics and physics, to see a reflection of a door located behind a person using a plane mirror, the mirror should be placed on either side of the person, allowing the light from the door to reflect into the person's line of sight by obeying the law of reflection.
Step-by-step explanation:
The subject of this question is Physics, specifically dealing with optics and the use of plane mirrors. To allow a person standing between a bookshelf and a door to see the door by reflection, one would need to place a plane mirror on the side of the person or the bookshelf so that the line of sight from the person's eyes can reflect off the mirror and onto the door behind them.
Given the nature of reflection, the light from the door will travel towards the mirror and reflect off it at the same angle, thus becoming visible to the observer. The image of the door will appear to be behind the mirror due to the law of reflection, which states that the angle of incidence equals the angle of reflection. This same principle is applied when considering how images are formed by optical instruments such as cameras or our own eyes.