[Lens] given: focal length and magnification, find image distance and image height

1. Dec 8, 2011

PhysicsGirl90

1. The problem statement, all variables and given/known data

With a lens with f = 25 cm, we want to project an image that is 5 times bigger than object, so M = 5

- Find the image distance s'
- Find the image height Hi

2. Relevant equations

1/f = 1/s + 1/s'

M = s'/s = Hi/Ho

With:
f = focus distance of lens
M = magnification
s' = image distance
s = object distance
Hi = image height
Ho = object height

3. The attempt at a solution

From the second equation we get: 1/s = M/s'

Substitute that in first equation to get s':

1/f = M/s' + 1/s' --> s' = (M+1)f = (5+1)*25 = 150 cm

The problem is now i don't know how to get the image height...from our answer we can easily calculate that s = 30 cm, so we know:

M = 5
f = 25 cm
s = 30 cm
s' = 150 cm

how do i get Hi?

2. Dec 8, 2011

netgypsy

Re: [Lens] given: focal length and magnification, find image distance and image heigh

You're missing the formula that related object and image distances to object and image heights

3. Dec 8, 2011

PhysicsGirl90

Re: [Lens] given: focal length and magnification, find image distance and image heigh

That is the second formula M = s'/s = Hi/Ho...but i only have s' and s, and i have to determine Hi

4. Dec 8, 2011

netgypsy

Re: [Lens] given: focal length and magnification, find image distance and image heigh

I think I'm brain dead. Can't you find one of the heights using the same technique you used finding the object and image distances?
You have M = Hi/Ho and you have s and s'
in terms of Hi and Ho to use in your focal length equation so you can make two equations I think. Try it.

Last edited: Dec 8, 2011
5. Dec 8, 2011

PhysicsGirl90

Re: [Lens] given: focal length and magnification, find image distance and image heigh

I don't think this excersise can be done...however i flip or turn it i always end up with M= Hi/Ho = 5....but with x/y = 5 we have two variables and one equation. I think the teacher made a mistake when he gave this excersise out.

6. Dec 8, 2011

netgypsy

Re: [Lens] given: focal length and magnification, find image distance and image heigh

I'll run it again in the morning. I did solve it but I could have made a mistake.

7. Dec 8, 2011

ehild

Re: [Lens] given: focal length and magnification, find image distance and image heigh

The object height is not given. You can say only that the image height is 5 times the object height.

ehild

8. Dec 9, 2011

netgypsy

Re: [Lens] given: focal length and magnification, find image distance and image heigh

Intuitively it didn't seem possible but I ran it a couple of times and didn't get anywhere either. If you draw a ray diagram using the given information I can't see that the information give in any way restricts the height of object and image other than one being 5 times larger than the other.