Question

A person standing 2.11 meters in front of a 21.7 cm tall plant sitting 13.0 cm in front of a plane mirror. The person now moves to a distance 5.50 meters in front of the plant. How tall does the image of the plant now appear in the mirror, in cm?

Answer 1

From the following ray diagram, the height of the plant in the mirror image remains the same when the person moves as well, but the apparent height ( or the angular height) chsnges

now from similiar triangles
initial angular size of plant = h/d
h = plant height = 21.7 cm
d = distance from plant image = a + 2b
a = distnace from plant = 2.11 m
b = distnac eof plant from mirrot = 12 cm
hence

initial angular size = 21.7/(211 + 2*12) = 0.092340425 rad
final angular size = 21.7/(550 + 2*12) = 0.037804878048 rad