Solve for Image Height: Find Hi with f, M, s & s

In summary, the student was having trouble solving an equation relating object and image distances to object and image heights. He was able to solve the equation relating object and image distances, but was not able to solve the equation relating image and object heights.
  • #1
PhysicsGirl90
17
0

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?
 
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  • #2


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


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:
  • #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


I'll run it again in the morning. I did solve it but I could have made a mistake.
 
  • #7


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

ehild
 
  • #8


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.
 

1. What do the variables f, M, s, and s stand for in the equation?

The variable f represents the focal length of the lens. M represents the magnification of the image. s represents the distance between the object and the lens, and s represents the distance between the lens and the image.

2. How is the image height (Hi) calculated using this equation?

The image height (Hi) is calculated by multiplying the magnification (M) with the object height (ho). This can be represented as Hi = M x ho.

3. What units are used for the variables in this equation?

The units used for the variables may vary depending on the system of measurement being used. However, the most common units used for f and s are meters, while M is unitless and ho is measured in the same units as the object height.

4. Can this equation be used for both convex and concave lenses?

Yes, this equation can be used for both convex and concave lenses. The only difference is that for a convex lens, f will be a positive value, while for a concave lens, f will be a negative value.

5. What is the significance of solving for image height in optics?

Solving for image height is an important aspect of optics as it helps determine the size and position of an image produced by a lens. This information is essential in fields such as photography, microscopy, and telescope design.

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