Question

A 2.0-cm-diameter spider is 1.8 m from a wall.

Determine the focal length f and position s′ (measured from the wall) of a lens that will make a half-size image of the spider on the wall.

Answer 1

1/f = 1/di + 1/do

where ,

do = distance from the lens to the object

di = distance from the lens to the image.

You want to project a real image,

so the image height hi and the object height ho will have different signs. You want the image height hi to be 1/2 the object height ho,

so
hi / ho = -1/2

= - si/so => 2 di = do
=>di + do = 1.8m

=> di + 2di = 1.8m
=> di = 0.6 m,

so, do = 2(0.6m) =1.2 m

now from the lens equation we have,

1/f = 1/(0.6) + 1/(1.2) = 2.5
=> f = 0.4 m