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?
Answer
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**
