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

  • #1

Homework Statement



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

Homework 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

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?
 

Answers and Replies

  • #2
246
1


You're missing the formula that related object and image distances to object and image heights
 
  • #3


That is the second formula M = s'/s = Hi/Ho...but i only have s' and s, and i have to determine Hi
 
  • #4
246
1


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.
 
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  • #5


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
246
1


I'll run it again in the morning. I did solve it but I could have made a mistake.
 
  • #7
ehild
Homework Helper
15,538
1,905


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

ehild
 
  • #8
246
1


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.
 
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