# Question with Three Thin Lenses Calculating for Final Image Distance

• Temp0
In summary, the problem involves three converging lenses with a focal length of 40.0 cm each, aligned on a common axis with a separation of 52.0 cm between adjacent lenses. The task is to find the position of the image of a small object located 80.0 cm to the left of the first lens. After using the equation 1/s + 1/s' = 1/f, the image is found to be between lens 2 and lens 3, 28 cm from lens 2 and 24 cm from lens 3. It is safe to assume that the lenses are converging based on the given focal length of 40 cm. The sign conventions for the object and image positions are not
Temp0

## Homework Statement

Three thin lenses, each with a focal length of 40.0 cm, are aligned on a common axis; adjacent lenses are separated by 52.0 cm.

Find the position of the image of a small object on the axis, 80.0 cm to the left of the first lens.

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

## The Attempt at a Solution

So I started this question out with doing:
1/80 + 1/s' = 1/40
solving for s' = 80.
However, my image ends up being between lens 2 and lens 3, 28 cm from lens 2 and 24 cm from lens 3. Now I'm stuck because I don't know what to do next. Any suggestions would be appreciated, thank you in advance.

Familiarize yourself with the sign convention used in lens calculations.

Hmm, but how do I know if it's a converging or diverging lens? I know that for a converging lens, focal length is positive and for a diverging one the focal length is negative. I assumed that the object is real so the distance s would be positive. However, the question doesn't state what type of lens I'm working with.

You're going to need to assume the type of lens you have here, otherwise you're going to have to consider 8 possible cases. Since the problem says the focal length is 40 cm and not -40 cm, I think you're safe going with converging lenses.

The sign conventions for the object and image only have to do with their positions relative to the lens. Don't worry about whether they're real or virtual.

I can provide you with a more detailed explanation of how to solve this problem. First, let's review the equation you used:

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

Where s is the object distance, s' is the image distance, and f is the focal length of the lens. In this case, we have three lenses with the same focal length, so we can simplify the equation to:

1/s + 1/s' = 1/40

Now, let's plug in the given values:

1/80 + 1/s' = 1/40

Solving for s', we get:

1/s' = 1/40 - 1/80
1/s' = 1/80
s' = 80 cm

This means that the image will be formed 80 cm to the right of the third lens. However, we also need to take into account the separation between the lenses. Since the object is 80 cm to the left of the first lens, we need to add 52 cm (the separation between the first and second lenses) to the image distance. This gives us a final image distance of 132 cm to the right of the first lens.

In summary, the image of the small object will be formed 132 cm to the right of the first lens, between the second and third lenses. I hope this helps clarify the solution for you. Keep up the good work in your studies!

## 1. How do I calculate the final image distance for a question with three thin lenses?

To calculate the final image distance, you can use the thin lens equation: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. You will need to apply this equation for each lens in the system, using the previous lens's image distance as the object distance for the subsequent lens.

## 2. What is the difference between a thick lens and a thin lens?

A thin lens is one in which the thickness of the lens is much smaller compared to the focal length. This allows us to simplify calculations by considering the lens to be a single point. A thick lens, on the other hand, has a significant thickness compared to the focal length and requires more complex calculations.

## 3. Can I use the thin lens equation for any type of lens system?

No, the thin lens equation can only be used for lens systems that are made up of thin lenses. For lens systems that include thick lenses or other optical elements, more advanced equations and techniques are needed to calculate the final image distance.

## 4. What is the significance of the final image distance in a three-lens system?

The final image distance tells us the location of the final image formed by the three-lens system. This is important in determining the magnification and size of the image, as well as its distance from the object and from the previous images formed by the lenses.

## 5. How can I verify my calculations for a three-lens system?

One way to verify your calculations is to use a ray diagram. Draw the principal rays for each lens, and see if they converge at the correct location for the final image. You can also check your results against known values or use computer simulations to compare your calculations.

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