Question

Whether the magnification is positive or negative in concave lens when the image is virtual and erect but it is in the opposite direction of incident ray

Answer 1

the negative and positive signs are not for the distance of the image from the lens. According to sign convention, the heights measured perpendicular to the x-axis above are positive and heights measured to the x-axis below are negative. Virtual images have the magnification as positive because they are erect and on the x-axis. Whereas, real images have the magnification as negative since the image formed is laterally inverted and are below the x-axis. So, virtual images will be positive and real images will be negative.


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Answer 2

The magnification is positive in concave lens when image is virtual and erect as according to sign convection we have

Heights measured upwards and perpendicular to the principle axis are taking positive and the heights measured downwards the principle axis are taken as negative.

So all images that are virtual are formed above the principle axis so magnification will be positive.

Now the virtual image and object both are at opposite of incident ray so we know magnification = distance of object/distance of image

Distance of object= -u

Distance of image= -v

Magnification =-u/-v so magnification is positive .

Hence when  image is virtual and erect so magnification is positive.