Diverging lens, calculating image location

In summary, using the thin lens equation, we can find the exact image location for a diverging lens with a focus of 2 meters, when the object is 3.66 meters away. The ray diagram may show a positive image distance, but according to the sign convention, the image should actually be 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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  • #2
The usual sign convention for thin lenses is such that the image distance is negative if the image is in front of the lens.
 

FAQ: Diverging lens, calculating image location

What is a diverging lens?

A diverging lens is a type of lens that causes parallel light rays to spread out or diverge. It is thinner at the center and thicker at the edges, causing the light rays to bend away from the central axis.

How do you calculate the image location of a diverging lens?

To calculate the image location of a diverging lens, you can use the formula: 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the object distance, and di is the image distance.

What factors affect the image location of a diverging lens?

The image location of a diverging lens is affected by the focal length of the lens, the distance of the object from the lens, and the refractive index of the material the lens is made of. Additionally, the curvature and thickness of the lens can also affect the image location.

Can a diverging lens produce a real image?

No, a diverging lens can only produce a virtual image, which is an image that appears to be behind the lens and cannot be projected onto a screen.

How do you know if the image produced by a diverging lens is upright or inverted?

The image produced by a diverging lens will always be upright, meaning it will have the same orientation as the object, regardless of the object's distance from the lens. This is because the light rays are always bent away from the central axis, causing the image to appear smaller and upright.

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