Question

in the derivation of lens formula we use sign convention rule once and again we use while solving problem the sign convention rule.Why

Answer 1

Sign convention is used just to make the problems easier and understandable ,
There is no restrictions on you while choosing sign conventions You can choose your own conventions but be careful while using them.

Answer 2

We have to use sign conventions because of the uses :

• To find the direction of image .

• To find direction of object.

• To distinguish the types of lens.

• To find the focal length .

• To find the position of object.

• To find position of image.

RULES

                         Note :

• f = focal length

• v = distance of image .

• u = distance of object .

Lens formula :

1 / f = 1 / v - 1 / u

Concave lens :

f = negative

u = negative

v =  negative

Convex lens

f = positive

u = negative

v = positive for real image ,

v = negative for virtual image .

The optical centre is chosen as the origin of the coordinate system.

With respect to optical centre :

The part which are above are positive, below negative.

The part which are right are positive while left is negative.

This is just like the normal x-axis and y-axis in the co-ordinate system .