# Final image distance using lenses

• kiwi101
In summary, a 15cm focal-length converging lens is placed 18cm to the right of a 4.0cm focal-length converging lens. An object with a height of 4.0cm is located to the left of the first lens. To find the value of s for the final image to be halfway between the two lenses, we can use the formula (1/s') + (1/s") = 1/f. Solving for s', we get a real image distance of 5.6cm formed by the first lens. However, this is not the same as the object distance for the second lens. To find the final value of s, we need to determine how far the object of the second
kiwi101
A 15cm focal-length converging lens is 18cm to the right of a 4.0cm focal-length converging lens. A 4.0cm tall object is distance to the left of the first lens.
For what value of is the final image of this two-lens system halfway between the two lenses?

My attempt:
I am working backwards:
s" = -9 (final virtual image displayed halfway between lenses)
f = 15
I solved for (1/s') + (1/s") = 1/f
s'= 5.6 cm (real image distance formed from lense 1)
f = 4cm
and now solve for s one more time and get s = 14
but that is wrong

kiwi101 said:
I solved for (1/s') + (1/s") = 1/f
s'= 5.6 cm (real image distance formed from lense 1)
s' is object distance for 2nd lens. That's not the same as the image distance for the 1st lens. If the object of the 2nd lens is 5.6 cm to the left of the 2nd lens, how far is that to the right of the 1st lens?

## 1. How do lenses affect the final image distance?

Lenses can either converge or diverge light rays, depending on their shape. This affects the path of light and ultimately determines the final image distance.

## 2. What factors influence the final image distance in lenses?

The curvature and thickness of the lens, as well as the distance between the object and the lens, all play a role in determining the final image distance.

## 3. Can the final image distance be negative?

Yes, the final image distance can be negative if the image formed by the lens is virtual or if the object is placed within the focal length of the lens.

## 4. How do you calculate the final image distance using lenses?

The final image distance can be calculated using the lens equation: 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the distance between the object and the lens, and di is the distance between the image and the lens.

## 5. Why is the final image distance important in lens design?

The final image distance is important in lens design because it determines the magnification and clarity of the image produced. It also helps in determining the optimal placement of the lens for a desired image size and quality.

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