The Floating Hologram · AI Generator #GEN-71D0C834
Physics · optics
Problem
A fascinating optical illusion device creates a "floating" hologram using a parabolic concave mirror and a small LED display. The mirror has focal length f=15.0cm and is positioned horizontally with its reflective surface facing upward. A small LED display of height h=2.0cm is placed below the mirror at a distance d from the mirror's vertex. When viewed from above, observers see what appears to be a three-dimensional image floating in mid-air above the mirror.
The illusion works because the mirror creates a real image that appears to hover above the mirror surface. For the effect to be most convincing, the real image should be positioned exactly 8.0cm above the mirror's vertex, and the image should appear upright to observers looking down from above.
(a) At what distance d below the mirror should the LED display be placed?
(b) What is the magnification of the image, and is it larger or smaller than the original display?
(c) What is the actual height of the floating image that observers see?