# Thin lens equation with multiple lenses

• frank48
In summary, the problem is to calculate the maximum magnification for a system of three lenses with focal lengths of 15.0, 20.0, and 25.0 cm when they are located 35.0 cm apart. The final magnification is the product of the linear and angular magnification, where the angular magnification is equal to 25 cm divided by the focal length. The lenses must be arranged in such a way that the first image is real and forms the object for the second lens, and then the configuration must be rearranged to evaluate the magnification for each case.
frank48

## Homework Statement

Heres the problem exactly as written:

A system of lenses is composed of three lenses. Calculate the maximum magnification these three lenses will achieve if the lenses are located 35.0 cm apart. The lenses have focal lengths of 15.0, 20.0, and 25.0 cm.

1/p + 1/q = 1/f
M = q/p = h`/h

## The Attempt at a Solution

I am confused on the maximum magnification part. It seems that would depend on where you placed the object or would it matter in which order the lenses are placed? An hints would be greatly appreciated.

The object would be outside the lens system and the virtual image would be viewed on the other side of the lense system. Switching the image position and the object would lead to the same answer due to symmetry. The problem is finding the arrangement of the three lenses such that a maximum magnification occurs. I'm assuming these are convex thin lenses thus forming a compound microscope. With this assumption the final magnification is the product of the linear magnification (which you showed) and the angular magnification which is

m angular = θ'/θ

where θ is approximately equal to h/near point of eye where near point of the eye is 25 cm and θ' = h/f so,

m angular = 25 cm/f

For a two lens compound mircoscope, the first image must be real in order to form the object for the second lens. Extend this to the three lens system. Then by brute force rearrange the configuration to evaluate the magnification for each case.

I would approach this problem by first understanding the thin lens equation and how it applies to multiple lenses. The thin lens equation, 1/p + 1/q = 1/f, describes the relationship between the object distance (p), image distance (q), and focal length (f) of a single lens. However, this equation can be applied to multiple lenses in a system by considering the combined focal length of the lenses.

In this problem, we have three lenses with focal lengths of 15.0, 20.0, and 25.0 cm. Plugging these values into the thin lens equation, we can calculate the combined focal length of the system:

1/15 + 1/20 + 1/25 = 0.1333 + 0.05 + 0.04 = 0.2233
1/f = 0.2233
f = 4.48 cm

Now, we can use the magnification equation, M = q/p, to calculate the maximum magnification of the system. Since the lenses are placed 35.0 cm apart, the object distance (p) would be 35.0 cm. The image distance (q) would be the distance between the last lens and the final image formed by the system. This can be calculated by adding the individual image distances for each lens:

q = 35.0 - 15.0 - 20.0 - 25.0 = -25.0 cm

Note that the negative sign indicates that the final image is formed on the same side as the object. Plugging these values into the magnification equation, we get:

M = (-25.0 cm)/(35.0 cm) = -0.714

Therefore, the maximum magnification achieved by this system of lenses is -0.714, which means the final image is inverted and smaller than the original object. The order in which the lenses are placed does not affect the maximum magnification, as long as they are placed in the same order and distance from each other. However, the position of the object and the distance between lenses can affect the final image and magnification. I hope this helps to clarify the problem.

## 1. What is the thin lens equation and how is it used in multiple lens systems?

The thin lens equation is a mathematical formula used to determine the relationship between the object distance (u), image distance (v), and focal length (f) of a single lens. In multiple lens systems, the equation can be used to calculate the overall magnification of the system by multiplying the individual magnifications of each lens.

## 2. How do you calculate the focal length of a multiple lens system?

The focal length of a multiple lens system can be calculated by adding the reciprocals of each individual lens' focal length: 1/f = 1/f1 + 1/f2 + 1/f3 + ... + 1/fn.

## 3. What is the difference between a converging and diverging lens in a multiple lens system?

A converging lens is thicker in the middle and causes parallel light rays to converge at a focal point, whereas a diverging lens is thinner in the middle and causes parallel light rays to diverge. In a multiple lens system, the combination of converging and diverging lenses can produce various magnifications and image types.

## 4. How do you determine the overall magnification of a multiple lens system?

The overall magnification of a multiple lens system can be calculated by multiplying the individual magnifications of each lens. The magnification of a single lens is equal to the ratio of the image distance to the object distance, or M = v/u. Therefore, the overall magnification is Mtotal = M1 x M2 x M3 x ... x Mn.

## 5. How does adding more lenses affect the overall magnification of a system?

Adding more lenses to a system can increase or decrease the overall magnification, depending on the individual magnifications of each lens. If the magnification of each lens is greater than 1, then adding more lenses will increase the overall magnification. However, if the magnification of each lens is less than 1, then adding more lenses will decrease the overall magnification. Additionally, the placement and combination of lenses can also affect the overall magnification of a multiple lens system.

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