(easy) Finding variables with mirror equation

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SUMMARY

The discussion centers on calculating the total magnification (Mtot) of a two-lens system where the first lens has a focal length (f) of 1.2 cm and the second lens has a focal length of 0.42 cm. The object is placed 1.3 cm from the first lens, resulting in a calculated image distance (di) of 15.6 cm and a magnification (M) of 12x for the first lens. The second lens, with an object distance (do) of 17.3 cm, yields an image distance of 0.43 cm and a magnification of 0.025x, leading to a total magnification of 0.3x, which is inconsistent with peers' results suggesting values in the 200s. The key error identified is the misunderstanding of how the image from the first lens serves as the object for the second lens.

PREREQUISITES
  • Understanding of lens formulas: di = dof/(do-f), M = di/do, Mtot = M1*M2
  • Familiarity with the concepts of object distance (do), image distance (di), and focal length (f)
  • Basic knowledge of magnification in optical systems
  • Ability to perform calculations involving multiple lenses
NEXT STEPS
  • Review the lens formula derivations for clarity on image formation
  • Study the concept of combined magnification in multi-lens systems
  • Practice problems involving two-lens systems with varying object distances
  • Explore the impact of changing focal lengths on total magnification
USEFUL FOR

Students studying optics, physics educators, and anyone preparing for assessments involving lens systems and magnification calculations.

classi
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This isn't exactly a homework problem, per se, but this was a district assessment I already took today. I was confident that I would get a good grade, but it turns out I got a measly 65%. I don't remember the exact wording, but I do remember the general idea of it.

Homework Statement


There are two lenses, both of which are 16cm apart. An object is 1.3cm away from the first lens.

First lens
f = 1.2cm
do = ?
di = ?
M = ?

Second lens
f = .42cm
do = ?
di = ?
M = ?

Total Magnification
Mtot = ?

Homework Equations


di = dof/do-f
M = di/do
Mtot = M1*M2

The Attempt at a Solution


First lens
f = 1.2cm
do = 1.3cm (given)
di = 15.6 cm
M = 12x

Second lens
f = .42
do = 16cm+1.3cm = 17.3cm
di = .43 cm
M = .025x

Total Magnification
Mtot = .3x
Looking back at it now, I think I messed up somewhere in the second lens.
I've asked friends what they got for Mtot, and the majority of them said a number around the 200s.

What am I doing wrong?
 
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classi said:
This isn't exactly a homework problem, per se, but this was a district assessment I already took today. I was confident that I would get a good grade, but it turns out I got a measly 65%. I don't remember the exact wording, but I do remember the general idea of it.

Homework Statement


There are two lenses, both of which are 16cm apart. An object is 1.3cm away from the first lens.

First lens
f = 1.2cm

Second lens
f = .42cm

Total Magnification
Mtot = ?

Homework Equations


di = dof/do-f
M = di/do
Mtot = M1*M2

The Attempt at a Solution


First lens
f = 1.2cm
do = 1.3cm (given)
di = 15.6 cm
M = 12x

Second lens
f = .42
do = 16cm+1.3cm = 17.3cm
di = .43 cm
M = .025x

Total Magnification
Mtot = .3x

Looking back at it now, I think I messed up somewhere in the second lens.
I've asked friends what they got for Mtot, and the majority of them said a number around the 200s.

What am I doing wrong?
Hello classi. Welcome to PF !

The image formed by the first lens becomes the object for the second lens.
 
Oh my gosh, thanks! :)
That makes perfect sense; I don't know why I didn't think of that before.
 

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