Diverging lens, calculating image location

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The discussion centers on calculating the image location for a diverging lens with a focal length of -2 meters and an object distance of 3.66 meters. The user applied the lens formula but obtained a negative image location of -1.29 meters, indicating the image is virtual and located in front of the lens. This aligns with the ray diagram, which confirms the image's position. The negative value for the image distance is consistent with the sign convention for thin lenses, where virtual images are represented as negative distances. The calculations and ray diagram support the conclusion that the image is indeed in front of the lens.
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Homework Statement



Diverging lens with focus of 2 meters. The object is 3.66 meters away from the lens. Find the exact image location.

Homework Equations



1/object + 1/image = 1/f

The Attempt at a Solution



I plugged in the numbers with a negative value for the focal length but I keep getting a negative value (-1.29 m) for my image location. However, when I do the ray diagram (which I'm confident is correct) I find that the image should be in front of the lens. Any explanations?
 
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The usual sign convention for thin lenses is such that the image distance is negative if the image is in front of the lens.
 
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