Must we always use absolute value for lens magnification?

[Jonforall]

My brother's physics teacher says that magnification and height of image are always positive. Is she right?

 

[kuruman]

My brother's physics teacher says that magnification and height of image are always positive. Is she right?

It depends on the context. It does not make sense to have a negative magnification if you look at it strictly as a factor by which an image is reduced or enlarged. However the usual definition of the magnification is a signed quantity $m = -(i/o)$ where $i$ and $o$ are, respectively, the distance of the image and object from the lens. The convention is that if the magnification thus defined is a negative number (both $i$ and $o$ are positive), the image is inverted and real; if the magnification is a positive number ($i$ is negative), the image is erect and virtual. This convention helps sort out whether images are real or virtual and inverted or erect and comes in handy when one considers the formation of images by multiple lenses. The height of an image is the magnification multiplied by the height of the object. Thus, the height of the object carries the sign of the magnification.

 

[Jonforall]

It depends on the context. It does not make sense to have a negative magnification if you look at it strictly as a factor by which an image is reduced or enlarged. However the usual definition of the magnification is a signed quantity $m = -(i/o)$ where $i$ and $o$ are, respectively, the distance of the image and object from the lens. The convention is that if the magnification thus defined is a negative number (both $i$ and $o$ are positive), the image is inverted and real; if the magnification is a positive number ($i$ is negative), the image is erect and virtual. This convention helps sort out whether images are real or virtual and inverted or erect and comes in handy when one considers the formation of images by multiple lenses. The height of an image is the magnification multiplied by the height of the object. Thus, the height of the object carries the sign of the magnification.

So should we always use absolute value in answering every problem that tells us to find height of image and its magnification?

 

[kuruman]

So should we always use absolute value in answering every problem that tells us to find height of image and its magnification?

Let me repeat: There is no "always" because it depends on the context. If the question gives you the focal length and the position of the object and asks for the magnification, I would include the negative sign. If instead the question asks "by what factor is the image smaller than the object?", I would not include the negative sign. The height of the image is usually positive although sometimes people who write a question asking for a height expect a negative sign to indicate that the image is inverted. This becomes important when you want to find the image formed by two of lenses in which the image formed by the first lens becomes the object for the second lens. Dropping the sign will get you in trouble. The upshot of all this is that only your instructor knows for sure what answer is expected, so ask.

 

[Jonforall]

Let me repeat: There is no "always" because it depends on the context. If the question gives you the focal length and the position of the object and asks for the magnification, I would include the negative sign. If instead the question asks "by what factor is the image smaller than the object?", I would not include the negative sign. The height of the image is usually positive although sometimes people who write a question asking for a height expect a negative sign to indicate that the image is inverted. This becomes important when you want to find the image formed by two of lenses in which the image formed by the first lens becomes the object for the second lens. Dropping the sign will get you in trouble. The upshot of all this is that only your instructor knows for sure what answer is expected, so ask.

Thanks