# Inserting thick lenses into a thin lens system and deducing values

• Kaelor
In summary: You need to adjust their positions to get the same image as before. You can try different distances and see what works. It's not about aligning the principal planes, it's about finding the right distance between the lenses to get the same result.
Kaelor
Homework Statement
Finding the distance between the back surface of the first lens and the front surface of the back lens.
Relevant Equations
1/f = 1/s_o + 1/s_i
Homework Statement:: Finding the distance between the back surface of the first lens and the front surface of the back lens.
Homework Equations:: 1/f = 1/s_o + 1/s_i

I have two positive thin lenses that are separated by a distance of 5 cm. The focal lengths of the lenses are F_1 = 10 cm and F_2 = 20 cm. I placed an object 2 cm to the left of the front focal point and calculated the image by using the equation 1/f = 1/s_o + 1/s_i twice, so that the image of the first lens became the object of the second lens.

See the attached images for an illustration of the thin lens system.
(credit to www.livephysics.com)

I am then told to insert two thick bi-convex lenses of 10 cm and 20 cm effective focal lengths into the system instead of the thin optical lenses, so that I get the same image with the same object 2 cm to the left of the front focal point. These thick lenses have all of the typical information available that one would find in a lens catalogue (radius of curvature, principal plane distances, refractive index, etc.), and I can provide this information if requested.

See the attached images for an illustration of the thick lens system.
(Note that d in this thick lens picture is different to the distance that I am describing below.)
(From Optics, Fifth Edition, by Hecht.)

I'm now trying to find the distance between the back surface of the first lens and the front surface of the back lens.

I have two problems:

1. I'm not sure that I'm correctly interpreting what is meant by inserting the thick lenses, so that one gets the same image with the same object 2 cm to the left of the front focal point.

2. Despite a tremendous amount of research, I don't understand how it is possible to infer the the distance between the two thick lenses that were inserted instead of the thin lenses. I wondered if I was just misunderstanding what is exactly meant by "inserting" thick lenses instead of thin lenses in a system, but I have looked through a lot of optics resources and found nothing that indicates that the lenses must be "inserted" in a specific way that allows for deduction of the distance. I am told that the distance is somewhere between 4 - 5 cm, but I don't understand how such a thing can be calculated. Since this value is so close to the original thin lens distance of 5 cm, this leads me to believe that I am completely misunderstanding something about the nature of thick lens systems and how they are "inserted" into a thin lens system. Could it be that, to "insert" a thick lens instead of a thin lens means to align the secondary principal plane of the first thick lens with the first thin lens, and align the primary principal plane of the second thick lens with the second thin lens, so that the distance between the secondary principal plane of the first lens and the primary principal plane of the second lens is 5 cm?

I would greatly appreciate it if people could please take the time to clarify this.

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Sounds like you are being asked to build an optically equivalent system to the thin lens one ... start with just sticking the thick lenses in arbitrary positions, find the front focal length, stick the object 2cm in front of that, find out where the image ends up.

It will be wrong ... so you need the lenses in different positions. Do they need them to be further apart or closer together?

You are being asked to use your understanding of lens systems to figure out how the front focal length and the resulting image position changes with the separation of the lenses.

I would not be reading a lot into the word "insert" here.
They just want you to use the thick lenses instead of the thin ones.

## 1. How do I calculate the value of the thick lens in a thin lens system?

To calculate the value of the thick lens in a thin lens system, you will need to use the thin lens formula (1/f = 1/u + 1/v), where f is the focal length of the thin lens, u is the distance of the object from the thin lens, and v is the distance of the image from the thin lens. You will also need to use the lensmaker's equation (1/f = (n-1)(1/R1 - 1/R2)), where n is the refractive index of the thick lens and R1 and R2 are the radii of curvature of the two surfaces of the thick lens. By combining these equations, you can deduce the value of the thick lens.

## 2. Can I use the same method for calculating the value of any thick lens in a thin lens system?

Yes, the thin lens formula and the lensmaker's equation can be used to calculate the value of any thick lens in a thin lens system. However, keep in mind that these equations assume thin lenses and do not take into account any aberrations that may occur in thick lenses.

## 3. What if the thick lens in my system is not symmetrical?

If the thick lens in your system is not symmetrical, meaning that its two surfaces have different radii of curvature, then you will need to use the generalized lens equation (1/f = (n1-n2)/n2 * (1/R1 - 1/R2)), where n1 and n2 are the refractive indices of the two media on either side of the thick lens. This equation takes into account the asymmetry of the lens and will give you a more accurate value.

## 4. How can I verify the accuracy of my calculated value for the thick lens?

One way to verify the accuracy of your calculated value for the thick lens is to perform a paraxial ray tracing. This involves tracing a few rays through the thin lens system and comparing the location of the final image to the calculated value. If they match, then your calculated value is likely accurate. Another way is to compare your calculated value to the manufacturer's specifications for the thick lens.

## 5. Are there any other factors that can affect the value of the thick lens in a thin lens system?

Yes, there are several other factors that can affect the value of the thick lens in a thin lens system. These include the thickness of the lens, the material properties of the lens, the wavelength of light passing through the lens, and any aberrations in the lens. It is important to take these factors into consideration when deducing values for thick lenses in thin lens systems to ensure accuracy.

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