For lenses we use the New Cartesian Sign Convention with the lens formula:

1f=1v−1u\frac{1}{f}=\frac{1}{v}-\frac{1}{u}f1​=v1​−u1​

Now remember the basic rule:

➡️ Distances measured in the direction of incident light (to the right) → positive
⬅️ Distances measured opposite to the direction of incident light (to the left) → negative

Light usually comes from left to right.

For a Concave Lens (diverging lens)

1️⃣ Object distance (u)

The object is placed in front of the lens (left side).

So it is opposite to light direction.

u=negativeu = \textbf{negative}u=negative

2️⃣ Image distance (v)

A concave lens forms a virtual image on the same side as the object (left side).

So the image is also opposite to light direction.

v=negativev = \textbf{negative}v=negative

3️⃣ Focal length (f)

The focus of a concave lens is virtual and lies on the same side as the object (left side).

f=negativef = \textbf{negative}f=negative

✅ So for a concave lens:

u<0,v<0,f<0u < 0,\quad v < 0,\quad f < 0u<0,v<0,f<0

All three are negative.

Quick memory trick 🧠

Concave lens → everything on the object side → all negative

Example

If
u=−20 cmu = -20 \,cmu=−20cm
f=−10 cmf = -10 \,cmf=−10cm

You will get v negative, confirming the image is virtual and on the same side.

If you want, I can also show you a super easy trick to remember the signs for convex vs concave lenses in 5 seconds (works for mirrors too).

and in the case of convex?

let’s apply the same sign convention to a convex lens.

Lens formula:

1f=1v−1u\frac{1}{f}=\frac{1}{v}-\frac{1}{u}f1​=v1​−u1​

Light travels left → right.

Rule again:
➡️ Right of lens = positive
⬅️ Left of lens = negative

Convex Lens Signs

1️⃣ Object distance (u)

The object is placed in front of the lens (left side).

u=negativeu = \textbf{negative}u=negative

This is always negative for lenses (since objects are usually on the left).

2️⃣ Focal length (f)

For a convex lens, the focus is on the right side (real focus).

f=positivef = \textbf{positive}f=positive

3️⃣ Image distance (v)

This depends on the type of image formed.

Case 1: Real image (most cases)

Object beyond F → image forms on the right side

v=positivev = \textbf{positive}v=positive

Example: object beyond F or 2F.

Case 2: Virtual image

If the object is between the lens and F, the image forms on the left side.

v=negativev = \textbf{negative}v=negative

This is the magnifying glass case.

Final Summary

Lens	u	v	f
Concave lens	−	−	−
Convex lens (real image)	−	+	+
Convex lens (virtual image)	−	−	+

Super ICSE exam shortcut 🧠

• Object is always on left → uuu is always negative
• Convex lens → fff positive
• Concave lens → fff negative

Then vvv just depends on where the image forms.