Total Magnification of Two Converging Lenses

In summary, the two lenses have a combined magnification of 0.715 when looking at an object 21 cm to the left of the left lens.
  • #1
aChordate
76
0

Homework Statement



Two identical converging lenses have focal lengths of 15 cm and are aligned on the
same principal axis. They are separated by a distance of 120 cm. An object sits a distance
of 21 cm to the left of the left lens. What is the total magnification of the two lenses?


Homework Equations



Thin lens equation
1/f=1/do+1/di

magnification equation
m=di/do

The Attempt at a Solution



Lens 1:
1/.15m=1/.21+1/di

d-i=0.525m

m=0.525m/0.21m=2.5

Lens 2:
1/.15=1/(.21+1.20m)+1/di

d-i=0.168m

m=0.80


m-total=0.80+2.5 ?
 
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  • #2
aChordate said:

Homework Statement



Two identical converging lenses have focal lengths of 15 cm and are aligned on the
same principal axis. They are separated by a distance of 120 cm. An object sits a distance
of 21 cm to the left of the left lens. What is the total magnification of the two lenses?


Homework Equations



Thin lens equation
1/f=1/do+1/di
That's the right equation. :smile:

magnification equation
m=di/do
You're missing a negative sign in there somewhere.

The Attempt at a Solution



Lens 1:
1/.15m=1/.21+1/di

d-i=0.525m
I think you mean "di" or di instead of "d-i". But whatever the case, your number is correct.

m=0.525m/0.21m=2.5
You're missing a negative sign somewhere.

Lens 2:
1/.15=1/(.21+1.20m)+1/di
Here is where things start to go south (read: here is where things start to go wrong).

You don't want to use the actual distance to the original object when evaluating the second lens. Instead, when evaluating the second lens, treat the image produced by the first lens as the "object."

It might help to draw a diagram.

Draw the first lens and the original object. Then draw the image created by the first lens. That image is the "object" that you will be using for the second lens.

d-i=0.168m

m=0.80
Of course you'll have to redo the image produced by the second lens. Use the image produced by the first lens as the second lens' object.

m-total=0.80+2.5 ?
When it does come time to combine the magnifications, you'll need to multiply the respective magnifications from the individual lenses, not add them. :wink:
 
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  • #3
On my second attempt I got an mtotal of 0.357
 
  • #4
aChordate said:
On my second attempt I got an mtotal of 0.357

I arrived at a different answer. :frown:

Could you show how you got your answer? Maybe I can help then.
 
  • #5
Lens 1:
1/.15m=1/.21+1/di

d-i=-0.525m

m=-0.525m/0.21m=-2.5

Lens 2:
1/.15=1/(.21+1.20m)+1/di

d-i=0.171m

m=-0.171/1.2m=-0.143


m-total=-2.5*-.143=0.357
 
  • #6
aChordate said:
Lens 1:
1/.15m=1/.21+1/di

d-i=-0.525m

m=-0.525m/0.21m=-2.5
Yes, so far so good. :approve:

Lens 2:
1/.15=1/(.21+1.20m)+1/di
Here's the problem. For the second lens, you are using the total distance all the way back to the original object for dO. Essentially, this is as through the first lens isn't even there! :eek:

Instead, you need to use the image produced by the first lens as the second's lens' object. You've already calculated that it lies 52.5 cm to the right of the first lens. This image of the first lens is what you want to use as the object of the second lens. :wink:
 
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  • #7
collinsmark said:
Yes, so far so good. :approve:


Here's the problem. For the second lens, you are using the total distance all the way back to the original object for dO. Essentially, this is as through the first lens isn't even there! :eek:

Instead, you need to use the image produced by the first lens as the second's lens' object. You've already calculated that it lies 52.5 cm to the right of the first lens. This image of the first lens is what you want to use as the object of the second lens. :wink:

Oops, I meant to correct that on the last attempt. Let me try again.

Lens 1:
1/.15m=1/.21+1/di

d-i=-0.525m

m=-0.525m/0.21m=-2.5

Lens 2:

do=1.20m-.525m=0.675m

1/.15=1/0.675m+1/di

d-i=0.193

m=-0.193m/1.2m=-0.161


m-total=-2.5*-0.161=0.402


I hope that's correct!
 
  • #8
aChordate said:
Oops, I meant to correct that on the last attempt. Let me try again.

Lens 1:
1/.15m=1/.21+1/di

d-i=-0.525m

m=-0.525m/0.21m=-2.5
So far so good, again. :approve:

Lens 2:

do=1.20m-.525m=0.675m

1/.15=1/0.675m+1/di

d-i=0.193
Also good! :smile:

m=-0.193m/1.2m=-0.161
Instead of using 120 cm as the distance to the object, use the distance of the first lens' image to the second lens. (Hint: you've already calculated this. This is the second lens' "object" distance. :wink:)
 
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  • #9
m=-0.193m/0.675m=-0.286

mtotal=-2.5*-.286=.715

thank you!
 
  • #10
aChordate said:
m=-0.193m/0.675m=-0.286

mtotal=-2.5*-.286=.715

thank you!

There you go. :smile:

(If you use more precision in your intermediate calculations, you might obtain a slightly better answer due to rounding; but your above answer is roughly correct.)
 

Related to Total Magnification of Two Converging Lenses

What is the definition of total magnification of two converging lenses?

Total magnification of two converging lenses refers to the overall increase in size of an object when viewed through two lenses in combination. It takes into account both the individual magnification of each lens and the combined magnification effect of the two lenses.

How is total magnification calculated for two converging lenses?

Total magnification is calculated by multiplying the magnification of the first lens by the magnification of the second lens. The magnification of a lens can be found by dividing the focal length of the lens by the distance between the object and the lens.

What factors affect the total magnification of two converging lenses?

The total magnification of two converging lenses can be affected by the individual magnification of each lens, the distance between the two lenses, and the distance between the object and the first lens. Other factors such as the curvature and thickness of the lenses can also play a role.

Can the total magnification of two converging lenses be greater than 1?

Yes, the total magnification of two converging lenses can be greater than 1. This means that the object will appear larger when viewed through the two lenses in combination than when viewed through a single lens.

How does the total magnification change if one of the lenses is removed?

If one of the lenses is removed, the total magnification will decrease since there is only one lens now magnifying the object instead of two. The magnification will also be affected by the removed lens's individual magnification and its position in relation to the other lens.

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