Magnification, when is it negative?

[izMuted]

Homework Statement

In magnification, I keep on confusing the signs. From what I understand currently, magnification is positive when the image is erect. An image is only erect when it is a virtual image, therefore virtual images = positive magnification. Vice versa, magnification is negative when the image is inverted, therefore a real image.

However using the equation m = v/u, m is negative when v is negative. And v is only negative when the image is on the same side of the lens as the object. Therefore meaning a virtual image (According to physicsclassroom "The negative value for image distance indicates that the image is a virtual image located on the object's side of the lens."). This contradicts the statement above where virtual images = positive magnification.

Where am I going wrong?

Homework Equations

m = v/u

The Attempt at a Solution

 

[Drakkith]

An image is only erect when it is a virtual image, therefore virtual images = positive magnification. Vice versa, magnification is negative when the image is inverted, therefore a real image.

That's only true for a single lens. A multi-element optical system can have positive magnification without the image being a virtual image. Consider a system which uses a relay lens. The objective generates an intermediate image which the relay lens then images, resulting in an upright final image of positive magnification. No virtual image necessary.

However using the equation m = v/u, m is negative when v is negative.

Assuming u is the distance between the lens and the object, then sign convention dictates that it should be negative. If you imagine the lens to be at the origin of a graph, then the object is to the left of 0, which is the negative direction. A virtual image would also be to the left and would also have a negative value for distance. The negatives would cancel out and the magnification would be positive.

 

[jtbell]

According to the sign convention that most introductory textbooks use, the magnification equation has a minus sign.

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lensdet.html#c2