Question

sign conventions both mirror and lens with sign...

Answer 1

Sign Convention for Spherical Mirrors:The following sign convention is used for measuring various distances in the ray diagrams of spherical mirrors:Object is always placed to the left of mirror. All distances are measured from the pole of the mirror.Distances measured in the direction of the incident ray are positive and the distances measured in the direction opposite to that of the incident rays are negative.Distances measured along y-axis above the principal axis are positive and that measured along y-axis below the principal axis are negative.

Answer 2

Spherical Mirrors
1)Focal Length (f) = + for concave mirrors  and - for convex mirrors 

2)Object Distance (u) = + if object is in front of the mirror (real object) and - if object is behind the mirror (virtual object)

3)Image Distance (v) = + if the image is in front of the mirror (real image) and - if the image is behind the mirror (virtual image) 

4)Magnification (m) = + for an image that is upright with respect to the object and - for an image that is inverted with respect to the object 

=======================================

Lenses 

1)Focal Length (f) = + for a converging lens and - for a diverging lens.

2)Object Distance (u) = + if the object is to the left of the lens (real object) and - if the object is to the right of the lens (virtual object)

3)Image Distance (v) = - if the object is to the right of the lens (virtual object) and + for an image (real) formed to the right of the lens by a real object 

4)Magnification (m) = + for an image that is upright with respect to the object and - for an image that is inverted with respect to the object.