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 42cm.

A) How many places can you put the lens to form a well-focused image of the candle flame on the wall? Answer: 2

B) What are the distance between the candle and the lens for each location? Answer: 60 and 140 cm

C) For each location, what is the height of the image? NEED ANSWER PLEASE SHOW WORK

lens equation

1/f = 1/Do + 1/Di

let D0 be x then

Di = 200-x

so,

1/42 = 1/x +1/(200-x)

x^2 - 200x = -8400

on solving this quadratic equation

we get,

x = 60 and 140

so we can put lens in two places to get well focused image

at 60 cm and 140 cm we can place candle

for x = 60

Do = 60

Di = 200-60

Di = 140

hi/ho = di/do

hi/4 = 140/60

height of image if object is places at 60 cm = 9.333 cm

for x = 140

Do = 140

Di = 200-140

Di = 60

hi/ho = di/do

hi/4 = 60/140

height of image if object is places at 140 cm = 1.7143 cm