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

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