Lens and mirror question, can't understand solution

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The discussion revolves around a problem involving a lens and a mirror, where confusion arises regarding the sign convention for image distances. The calculations show that the image formed by the lens is 4.0 m behind the lens, leading to a negative object distance for the mirror. The second image distance calculated for the mirror is -0.6 m, indicating it is behind the mirror. The confusion stems from the final image distance for the lens, which is calculated as positive 1.6 m, despite the object being to the right of the lens. Clarification is needed on the sign conventions used, particularly when light travels from right to left, affecting the interpretation of distances.
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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 postive 1.6 m instead of negative 1.6 meters? The "object" is to the right of the lens, so shouldn't di3 be negative?
 
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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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