# Lens Power Calculator

 Lens Power dioptre Refractive Indexlens Refractive Indexmedium Radius1 mpmnmmicrons (µm)mmcmkmmilinchesfeetyardsmilesPlanckBohrsAngstromlight-secondslight-yearsauparsecspointscubitsfathomsrodschainsleagues Radius2 mpmnmmicrons (µm)mmcmkmmilinchesfeetyardsmilesPlanckBohrsAngstromlight-secondslight-yearsauparsecspointscubitsfathomsrodschainsleagues Please enter valid input

## 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 = (nl/nm – 1) * ( 1/r1 – 1/r2)

where :

P: Power of lens

f: Focal Length, in meter

nl: Refractive Index of Lens Material, in meter

nm: Refractive Index of Ambient Medium, in meter

r1: Curvature Radius of the First Surface, in meter

r2: 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. :

nl = 1.50,nm = 1, r1 = 10cm and r2 = -15cm

1/f = (nl/nm – 1) * ( 1/r1 – 1/r2)

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 = nl – 1/ r1

where :

P: Surface Power

nl: Refractive Index of Lens Material, in meter

r1: 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.

Pn = P1 + P2

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 = P1 + P2

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.