physics help needed !?

A 4.0 cm tall candle flame is 2.0 m from a wall. You happen to have a lens with a

focal length of 32 cm. How many places can you put the lens to form a well-focused

image of the candle flame on the wall? For each location, what are the height and

orientation of the image

Answer:

s = 200 – s’

1/s + 1/s’ = 1/f

1/(200 – s’) + 1/s’ = 1/32

s’ = 40 cm

s’ = 160 cm

for s’ = 40 cm ⇒ s = 160 cm

h’/h = s’/s

h’/4 = 40/160

h’ = 1 cm

for s’ = 160 cm ⇒ s = 40 cm

h’/h = s’/s

h’/4 = 160/40

h’ = 16 cm