**Lens Power Calculator**

Lens Power |
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Refractive Index_{lens} |
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Refractive Index_{medium} |
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Radius_{1} |
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Radius_{2} |
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## Definition

The ability to converge/diverge the rays of light is known as Lens Power.

The power of a lens is measured by the reciprocal of its focal length, **P = l / ƒ **where f is the focal length of lens

Power of combination of n thin lenses in contact: Pn = P1 + P2 + ………Pn

Power of **convex lens** is positive and **concave lens **is negative

## Formula

Power of a lens is given by Lensmaker’s Equation formula:

P = 1/f = (n_{l}/n_{m} – 1) * ( 1/r_{1} – 1/r_{2})

where :

P: Power of lens

f: Focal Length, in meter

n_{l}: Refractive Index of Lens Material, in meter

n_{m}: Refractive Index of Ambient Medium, in meter

r_{1}: Curvature Radius of the First Surface, in meter

r_{2}: Curvature Radius of the Second Surface, in meter

**Note – **This equation holds for all types of thin lenses. If Lens is not immersed in Ambient Medium, value of Refractive Index of Ambient Medium is “1”. A radius of curvature is positive when its center of curvature lies to the right of the surface, and negative when its center of curvatures lies to the left of the surface

**Example**

1. The refractive index of a lens is given as 1.5, two curved surfaces have radius of curvature 10cm and -15cm respectively. Calculate the power of the given lens?

**Sol. :**

n_{l} = 1.50,n_{m} = 1, r_{1} = 10cm and r_{2} = -15cm

1/f = (n_{l}/n_{m} – 1) * ( 1/r_{1} – 1/r_{2})

1/f = (1.50 -1) * (1/10 + 1/15)

1/f = 0.5 * (0.1 + 0.0666) = 0.5 * 0.1666 = 0.0833

f= 1/0.0833 cm = 12 cm

f = 12/100 m = 0.12 m

So, Lens Power, **P = 1/f = 8.33 Dioptre**

**Surface Power : **p = n_{l} – 1/ r_{1}

where :

P: Surface Power

n_{l}: Refractive Index of Lens Material, in meter

r_{1}: Curvature Radius of the First Surface, in meter

**Nominal Power : **For Lens in close contact, the power of the combined Lens is equal to the sum of their individual Lens Powers.

P_{n} = P_{1} + P_{2}

**Example:**

1. What is the power of concave lens of focal length 4m?

**Sol. :**

P = 1/f

P = 1/4

**P = .25D**

Since it is power of **concave lens, therefore P = -.25D**

2. Two lens of power +3.0D and -1.5 are placed in contact .Find the power of the combination of lens?

**Sol. :**

P = P_{1} + P_{2}

P = (+3.0) + (-1.5)

**P = +1.5D**

## Units

The standard unit of measurement for lens power is **dioptre**.

**One dioptre** is the power of a lens whose focal length is 1 meter.