Why does +64.7 cm suddenly turn to -64.7 meters in the work here for object dist

Question

Why does +64.7 cm suddenly turn to -64.7 meters in the work here for object distance? I understand that the converging lens forms a real, inverted image which is to the right of the converging lens, but do we just add the negative on there because we know it's a converging lens, even if the answer comes out as a positive from 1/f=1/do+1/di?

Also, how do we know that this image distance of -64.7, which becomes the object distance for the second diverging mirror, is still to the left of the second mirror? And why do we hadd 30 to it?

If someone could please draw a picture, I think it would help tremendously. Thank you.

Explanation / Answer

Converging lens forms a real, inverted image , this is because the image is real we have taken the negative value .

For , the virtual image sign convention is positive .

30 is added to the image distance because the distance is calculated from the centre of the second mirror .

Image distance of -64.7 is calculated from the centre of first mirror .

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