Power Calculators

🔍 Lens Formula Calculator (1/v − 1/u = 1/f)

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Negative: the object is on the left of the lens.
Positive for a convex lens, negative for a concave lens.
Image distance v (cm)
-12
Magnification m
0.4
Power of the lens (D)
-5

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📘 About the Lens Formula

The lens formula relates the object distance u, the image distance v and the focal length f of a thin lens. This calculator uses the New Cartesian sign convention taught in Class 10 and 12 NCERT physics: distances are measured from the optical centre, left is negative and right is positive.

A positive image distance means a real image on the other side of the lens; a negative one means a virtual image on the same side as the object. A negative magnification means the image is inverted; a size bigger than 1 means it is enlarged.

🧮 Formula

Lens formula
1/v − 1/u = 1/f
Magnification
m = v ÷ u = h′ ÷ h
Power
P = 1 ÷ f (metres)

Where

  • u = object distance (negative for a real object)
  • v = image distance (+ real image, − virtual image)
  • f = focal length (+ convex, − concave)
  • m = magnification (− inverted, + upright)
  • P = power in dioptres (D)
Sign convention: distances measured in the direction of the incident light (left to right) are positive.

✏️ Worked examples

Convex lens, object at 30 cm, f = 20 cm

You enter
Object distance (u)-30 cm
Focal length (f)20 cm
You get
Image distance v (cm)60
Magnification m-2
Power of the lens (D)5

The image forms 60 cm behind the lens; m = -2, so it is real, inverted and twice the size.

Try this example →

Concave lens, object at 30 cm, f = −20 cm

You enter
Object distance (u)-30 cm
Focal length (f)-20 cm
You get
Image distance v (cm)-12
Magnification m0.4
Power of the lens (D)-5

The image is at -12 cm (virtual, same side), with m = 0.4: upright and smaller.

Try this example →

🧭 How to use this calculator

What you enter

  • Object distance (u) (cm)Negative: the object is on the left of the lens.
  • Focal length (f) (cm)Positive for a convex lens, negative for a concave lens.

What you get

  • Image distance v (cm)
  • Magnification m
  • Power of the lens (D)

💡 Images formed by a convex lens

  • Object beyond 2F: image between F and 2F, real, inverted, smaller.
  • Object at 2F: image at 2F, same size.
  • Object between F and 2F: image beyond 2F, enlarged.
  • Object at F: image at infinity.
  • Object between F and the lens: virtual, upright, enlarged (magnifying glass).

❓ Frequently asked questions

What is the lens formula?

1/v − 1/u = 1/f, using the New Cartesian sign convention.

What is the magnification of a lens?

m = v/u. A negative m means the image is inverted; |m| > 1 means it is enlarged.

What is the power of a lens?

P = 1/f with f in metres, measured in dioptres. A convex lens has positive power; a concave lens negative.

Why is u negative?

Under the sign convention the object is placed to the left of the lens, against the positive direction.