Lens and mirror question, can't understand solution

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SUMMARY

The discussion revolves around a physics problem involving a lens with a focal length of 0.8m and a mirror with a focal length of -0.500m. The object is positioned 1.0m to the left of the lens, and the solution involves calculating the image distances using the lens formula 1/f = 1/di + 1/do. The confusion arises in determining the sign of the final image distance (di3) for the lens after light reflects off the mirror, with the correct value being 1.6m, indicating the image is formed on the same side as the object relative to the lens.

PREREQUISITES
  • Understanding of the lens formula: 1/f = 1/di + 1/do
  • Knowledge of sign conventions in optics for lenses and mirrors
  • Familiarity with focal lengths of lenses and mirrors
  • Basic principles of light reflection and refraction
NEXT STEPS
  • Study the derivation and applications of the lens formula in optics
  • Learn about the sign conventions for lenses and mirrors in detail
  • Explore the concept of virtual and real images in optical systems
  • Investigate the behavior of light in multi-element optical systems
USEFUL FOR

Students studying optics, physics educators, and anyone seeking to understand the behavior of light in systems involving lenses and mirrors.

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Homework Statement


A lens of focal length 0.8m is 1.0 m to the left of a mirror of focal length -0.500m. An object is placed 1.00 m to the left of the lens. Light goes through the lens, bounces from the mirror, and goes through the lens again, this time from the right.


Homework Equations



1/f=1/di+1/do

The Attempt at a Solution



(THIS IS FROM THE OFFICIAL SOLUTION MANUAL, I AM CONFUSED ON PART OF THE ANSWER TOWARDS THE END)
1/di1=1/f1-1/do1
1/di1=1/0.8-1/1
di1=4.0 m

This image is 3 meters behind the mirror, so do2 for the mirror is -3.0 m.

1/di2=1/f2-1/do2
1/-0.5-1/-3=1/di2
di2= -0.6 m

This image is behind the mirror.

THIS IS WHERE I GET CONFUSED:
di3 (for the lens)=1+0.6m=1.6m

1/di2=1/f1-1/do3=1/0.8-1/1.6
di3=1.6m

In this instance, why is di3 positive 1.6 m instead of negative 1.6 meters? The "object" is to the right of the lens, so shouldn't di3 be negative?
 
Physics news on Phys.org
If light is moving from left to right than left is positive and right is negative (that's the convention for an object), but if light is moving from right to left (and that's the case here) than right is positive and left is negative.
 

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