Determine the focal length of a lens

[rayhan619]

Homework Statement

A 2.0-cm-diameter spider is 2.0 {\rm m} from a wall.
Determine the focal length of a lens that will make a half-size image of the spider on the wall.
Determine the position (measured from the wall) of a lens that will make a half-size image of the spider on the wall.

Homework Equations

M = fi/fo = di/do
1/f = 1/do + 1/di

The Attempt at a Solution

i got the first part. but not sure how to do the second one

 

[Delphi51]

How did you get the first part? What did you get? There appear to be an infinite number of solutions, so I'm wondering which one you chose.

 

[rayhan619]

that was in the book. I am not really sure how to get that.
i tried it but i got -2m as the focal lens, where it is supposed to be 0.44m
here is how i did it

M = hi/ho
0.5 = hi/0.02
hi = 0.01 m

hi/ho = -di/do
0.01/0.02m = -di/2m
di = -1m

1/f = 1/do+1/di
1/f = 1/2m+1/-1m
f = -2 m

im not sure where i messed up

 

[Delphi51]

hi/ho = -di/do
0.01/0.02m = -di/2m
di = -1m

You chose Do = 2 m.

Oh, I missed that - the image is on the wall 2m from the spider! So the lens must be between the wall and the spider. And Do + Di = 2. Between the two of us, we'll get this yet!
You can't choose Do = 2; you must put Do = 2 - Di.
Probably easiest to put it into 1/2 = Di/Do so you can solve for Di.
Then it is easy to get f. I get a little less than half a meter.
Kind of backwards, having to do (b) before (a).

 

[rayhan619]

got it
thanx a lot