New Cartesian Sign Convention

Picture the mirror or lens sitting at the origin of a graph. For a mirror the origin is its pole. For a lens it is the optical centre. The object is always placed on the left. The rules follow from that picture:

• All distances are measured from the pole or the optical centre.
• Distances to the right are positive. Distances to the left are negative.
• Heights above the principal axis are positive. Heights below it are negative.

So the object distance u is always negative. A convex lens has a positive focal length, and a concave lens a negative one.

A small example

A concave mirror has a focal length of 10 cm. An object stands 30 cm in front of it. Both lie to the left, so u = -30 cm and f = -10 cm. The mirror formula then gives v = -15 cm. The minus sign says the image is also in front of the mirror, so it is real.

Where marks go

Question 35 of CBSE's 2026-27 Science sample paper uses a concave lens. The object is 24 cm away and the image is one-third its size. The 2026-27 Science marking scheme writes u = -24 cm and m = +1/3, because the image is upright. It gives 1 mark for v = -8 cm and 1 mark for f = -12 cm.

Both marks rest on the signs. A plus where a minus belongs changes every number after it. Read how step marking treats each line of working.

About the author

Deepti Sardana

Founder Member & Academic Lead

An IIT alumna (M.Sc., M.Phil.) with over 25 years in teaching, child psychology and learning assessment. As Academic Lead at EduBrahma, she leads the method TRUtesting uses to find where and why a child loses marks.

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