The Periscope Artist's Dilemma · AI Generator #GEN-7D181898
Physics · optics
Problem
A street artist uses a simple periscope made of two plane mirrors to observe and sketch people on a busy plaza from her hidden position in a nearby café. The periscope has two plane mirrors, each inclined at 45° to the horizontal, separated by a vertical distance of h=80cm. She notices that when she looks through the periscope at a person standing d=12m away from the upper mirror, the person appears to be at a different distance than expected.
(a) What is the total optical path length traveled by light from the person to the artist's eye through the periscope?
(b) If the artist's eye is positioned 25cm behind the lower mirror, at what apparent distance does the person seem to be from her eye? (Assume the mirrors introduce no additional optical effects beyond simple reflection.)