How Do You Calculate Image Position with Two Converging Lenses?

[Kay Oss]

Homework Statement

Two converging lenses, each of focal length
14.7 cm, are placed 39.7 cm apart, and an
object is placed 29.3 cm in front of the first.
How far from the first lens is the final image
formed? What is the magnification of the system?
Answer in units of cm.

Homework Equations

1/f = 1/di + 1/do

do is the distance to the object from the lens while di is the distance of the image from the lens

M = - di/do

The Attempt at a Solution

I know:
f₁ = 14.7
f₂ = 14.7
do₁ = 29.3
separated by 39.7

to find di₁:

1/( 1/f₁ - 1/do₁) = 29.50068493

To find do₂ I did the separeted - di₁ to get 10.19931507

Finally di₂ = 1 / ( 1/14.7 - 1/10.19931507) = -33.31269215

To find the image position I added 39.7 + (-33.31269215) + 29.50068493 = 35.88799278 I enter this as my final answer but got it wrong. I thought that possibly di₂ should be positive. I added again to get 102.5133771 but this answer was also wrong.

 

[Redbelly98]

Welcome to Physics Forums.

The Attempt at a Solution

I know:
f₁ = 14.7
f₂ = 14.7
do₁ = 29.3
separated by 39.7

to find di₁:

1/( 1/f₁ - 1/do₁) = 29.50068493

To find do₂ I did the separeted - di₁ to get 10.19931507

Finally di₂ = 1 / ( 1/14.7 - 1/10.19931507) = -33.31269215

Looks okay so far.

To find the image position I added 39.7 + (-33.31269215) + 29.50068493 = 35.88799278 I enter this as my final answer but got it wrong.

di₂=-33.3 cm is the image position with respect to the second lens. The first lens is 39.7 cm from the 2nd lens. The 29.5 cm isn't part of this calculation.