# Calculate the focal distance of the duplicate

• Karl Karlsson
In summary, the conversation discusses the design of a chromatic doublet lens, which consists of two lenses with different curvatures and refractive indices, placed close together to minimize chromatic aberration. The focal distance of the duplicate is calculated by using the standard strategy for solving compound lens problems, where an object is placed at a finite distance in front of the combination and the position of the final image is found. The calculation should take into account the air gap between the lenses.

#### Karl Karlsson

Homework Statement
Calculate the focal distance of the duplicate
Relevant Equations
Lensmaker's equation
The picture below shows a so-called chromatic doublet, which is designed to minimize chromatic aberration, ie the wavelength dependence of the refractive index of the glass. The first lens has a flat first surface and a concave second surface with radius of curvature R and index of refraction n1 . The second lens is double convex with curvature radius R (refraction index n2) and sits close to the first lens. The lenses can be considered thin.

Calculate the focal distance of the duplicate

My try:

I seem to be getting the wrong answer. What am i doing wrong?

Correct answer is R/(2*n2 - n1 - 1)

#### Attachments

• IMG_0590.jpeg
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What did you use for the focal length of the second lens? Note that the figure shows a clear air gap between the two lenses. This means that you should find the two focal lengths as if the lenses were surrounded by air.

On edit: You need to adopt the standard strategy for solving compound lens problems of this kind: (a) Put an object at some finite distance ##s## in front of the combination; (b) find the position of the image ##s'##; (c) Treat the image as the object for the second lens (pay close attention to what is real and what is virtual); (d) find the position of the final image ##s''##; (e) let ##s## go to infinity and see what ##s''## becomes; (f) relate ##s''## to the focal length of the combination.

I tried this method for this problem and got the answer you quoted as correct.

Last edited:
Why does ##n_1## appear in the formula for lens 2 while ##n_2## does not appear in the formula for lens 1 ?

Does close together mean zero in between ?

kuruman said:
What did you use for the focal length of the second lens? Note that the figure shows a clear air gap between the two lenses. This means that you should find the two focal lengths as if the lenses were surrounded by air.

On edit: You need to adopt the standard strategy for solving compound lens problems of this kind: (a) Put an object at some finite distance ##s## in front of the combination; (b) find the position of the image ##s'##; (c) Treat the image as the object for the second lens (pay close attention to what is real and what is virtual); (d) find the position of the final image ##s''##; (e) let ##s## go to infinity and see what ##s''## becomes; (f) relate ##s''## to the focal length of the combination.

I tried this method for this problem and got the answer you quoted as correct.
My bad I can see my mistake as you pointed out now. I didn't think of the air gap between the lenses. Thanks!

## 1. What is the formula for calculating the focal distance of the duplicate?

The formula for calculating the focal distance of the duplicate is: f = (d x D)/d + D, where f represents the focal distance, d represents the distance between the original object and the lens, and D represents the distance between the lens and the duplicate.

## 2. How do I measure the distance between the original object and the lens?

To measure the distance between the original object and the lens, simply use a ruler or measuring tape to determine the exact distance in centimeters or inches.

## 3. Can I use any unit of measurement for the distance values in the formula?

Yes, you can use any unit of measurement as long as you are consistent throughout the calculation. However, it is recommended to use the same unit for both distances for accuracy.

## 4. Do I need to take any special precautions when calculating the focal distance of the duplicate?

Yes, it is important to make sure that the lens and the duplicate are aligned properly and that there is no movement or shaking during the measurement. Also, make sure to use accurate distance values for precise results.

## 5. What can the focal distance of the duplicate tell us?

The focal distance of the duplicate can tell us the distance at which the image of the original object will be formed by the lens. This is important in understanding the magnification and quality of the duplicate image.