# Double Lens System: Converging/Diverging

Venerable R

## Homework Statement

Image: http://i.imgur.com/NMS7BUK.jpg?1

a) Find the position of the final image of the 1.0-cm-tall object.
b) Find the size of the final image of the 1.0-cm-tall object.

h = 1 cm
f1 = 5 cm
do = 4 cm
f2 = -8 cm
L = 12 cm
di = ?

## Homework Equations

1/f = 1/do + 1/di

## The Attempt at a Solution

a) di1 = 1/(1/f1 - 1/do) = 1/(1/5cm - 1/4cm) = -20 cm (virtual image through a converging lens?)
di2 = 1/(1/f2 - 1/(l - do)) = 1/(1/-8cm - 1/(12-(-2))) = -6.4 cm

This answer is not right. I would really appreciate any help with double lens systems. We're covering them now in class, and I'm very confused by optics!

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Homework Helper
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a) di1 = 1/(1/f1 - 1/do) = 1/(1/5cm - 1/4cm) = -2 cm

Check the above calculation.

[EDIT: I think this might just be a typo. I also get -6.4 cm for the image distance of the second lens. Did the question state how the answer should be given? That is, are you supposed to give the answer relative to the second lens or relative to the first lens?]

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• Venerable R
Venerable R
Check the above calculation.

[EDIT: I think this might just be a typo. I also get -6.4 cm for the image distance of the second lens. Did the question state how the answer should be given? That is, are you supposed to give the answer relative to the second lens or relative to the first lens?]

Oh! It's the distance from the object! So, I added 4 cm + (12 cm - 6.4 cm) which gave me the correct answer of 9.6 cm. (Also: Yep, that was a typo!)

Thank you! :D

DrewHizzy
I have this same problem, and I also get di1 as -20cm, what am I missing? I'm having trouble determining what "do2" I should use in the second calculation? How do I get there?

Homework Helper
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-20 cm is correct for di1. The image of the first lens is treated as the object of the second lens.

DrewHizzy
-20 cm is correct for di1. The image of the first lens is treated as the object of the second lens.
I get that far but when I do the calculation, the answer is wrong. 1/f - 1/di1 = 1/di2 --> 1/-8 - 1/-20 = 1/di2 --> -5/40 - (-2/40) = 1/di2 --> 40/-3 = di2 =.13.3333cm , which is incorrect according to previous replies in this forum.

Homework Helper
Gold Member
When you treat the image of the first lens as the object of the second lens, it doesn't mean that the image distance of the first lens equals the object distance for the second lens.

Draw a diagram. Locate the image of the first lens in your diagram. If that image is treated as the object of the second lens, then what should you use for the object distance for the second lens?

DrewHizzy
Again, this is the piece I do not understand.

Homework Helper
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Can you describe in words what it means to say that the image distance of the first lens is -20 cm?

DrewHizzy
If the lens equation gives a negative image distance, then the image is virtual on the same side of the lens as the object?

Homework Helper
Gold Member
Yes. So, where did you draw the image of the first lens?

DrewHizzy
Yes. So, where did you draw the image of the first lens?
Would it be to the left of the first lens?

Homework Helper
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Yes. How far to the left of the first lens?

DrewHizzy
16cm left?

Homework Helper
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No. How did you get that?

DrewHizzy
No. How did you get that?
20 - 4 since do was already 4cm away from the first lens? Clearly I do not understand, any real explanation you could give would help..

Homework Helper
Gold Member
You need to review the basic definition of "image distance of a lens (di)". It's defined to be the distance from the lens to the image (with images on the left defined as having negative image distances).

So, when you find that di1 = -20 cm, where is the image of the first lens located in relation to the first lens?

DrewHizzy
You need to review the basic definition of "image distance of a lens (di)". It's defined to be the distance from the lens to the image (with images on the left defined as having negative image distances).

So, when you find that di1 = -20 cm, where is the image of the first lens located in relation to the first lens?
20cm left of the first lens

Homework Helper
Gold Member
Yes. Good. So, next you treat this image of the first lens as the object of the second lens. What should you use for do2?

DrewHizzy
-20cm - 12cm(distance b/w lenses), -32cm?

Homework Helper
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Almost. What is the sign convention for object distances?

DrewHizzy
Almost. What is the sign convention for object distances?
POSITIVE 32cm! --> 1/-8 - 1/32 = 1/di2 --> -4/32 - 1/32 = 1/di2 --> di2 = 32/-5 = -6.4cm

Homework Helper
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That's it. Good.

DrewHizzy
That's it. Good.
Thanks for all your help. So for final position, it's relative to the original object correct?

Homework Helper
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Apparently the question asks for the distance between the image of the second lens and the object of the first lens. See post #3. Did you get an answer for that?

DrewHizzy
Apparently the question asks for the distance between the image of the second lens and the object of the first lens. See post #3. Did you get an answer for that?
Two calculations are required, hi1/ho = -di/do for the first lens yields 5cm, then hi2/hi1 = - di2/di1 = 1.0 cm, correct answer

Homework Helper
Gold Member
Two calculations are required, hi1/ho = -di/do for the first lens yields 5cm,
The 5 cm that you are getting represents the height of the image of the first lens? If so, OK.

then hi2/hi1 = - di2/di1 = 1.0 cm, correct answer
The di1 should be do2. Also, note that the ratio hi2/hi1 is dimensionless, so it does not have units of cm.

DrewHizzy
About the di1 being do2, that's what I was thinking I was just unsure which notation was more accurate

Homework Helper
Gold Member
If you want to make sure you are thinking correctly about the second part of the question, try answering the following questions?
(1) What is the magnification of the first lens alone?
(2) What is the magnification of the second lens alone?
(3) What is the magnification of both lenses together?
(4) How do you use the result of question (3) to determine the height of the final image?