Power of a Lens

Introduction

Before learning about the power of the lens, we have to understand the term lens. Lens is a piece of glass or transparent material which is usually circular and has two surfaces that are polished in a specific manner for converging and dispersing of light rays.

The greater the power of the lens, the greater is its ability to refract the light that passes through it.

“The power of a lens is the measure of convergence or divergence of a lens”. In simple words, power is basically how much it can converge or diverge the ray of light that is coming toward it. The converging capability of a convex lens and diverging capability of a concave lens is called the power of a lens.

Power of a Lens Formula

To find the power of the lens, we can use the below formula: 

                                     P = 1 / F (meter) 

Where, P is the power of the lens and F is focal length. 

The SI unit of power is in meter inverse which is also known as Diopter (D).  

If the focal length is in meters then the power of the lens is measured in diopters.

You should know, 

converging (convex) lenses have positive focal length thus the power of converging lens is positive whereas the diverging (concave) lens have negative focal length, so the power value of diverging lens is negative. 

Note: The power value of the plane glass plate is zero. 

Power of lens when immersed in a medium of refractive index

Let’s discuss the refractive index to understand the power of lenses in a medium. 

Refractive index is also called the index of refraction in ray optics and its value is used in optical physics. It is simply defined as the measurement of bending of light rays falling on the medium and passing from one medium to another medium. 

Refractive index equals the velocity of light in vacuum, that is C of given wavelength divided by its velocity of light in a medium. 

Mathematically it is written as, 

n = c / v 

where, n is the refractive index, c is speed of light in vacuum, and v is velocity of light in medium. 

Power of lens in a medium

To find the power of a lens in a medium, we can use the following formulas. 

Power of the lens is equal to the refractive index of any medium other than air which is divided by its focal length. 

P = n / f….equation (1).  

Secondly by lens maker formula which shows relation between focal length of lens and its refractive index. 

             1/ f  = (n1/n2 – 1) (1/ R1 – 1/R2) 

Where, f is the focal length (half of the radius of curvature) 

             n1 is the refractive index of the surrounding medium 

             n2 is the refractive index of glass medium  

             R1 is the radius of curvature of first surface of lens 

             R2 is the radius of curvature of second surface of lens 

                n1/f  = (n2 – n1) (1/R1 – 1/R2) 

P  = (n2 – n1) (1/R1 – 1/R2 ) …..by equation 1 

By the above formula we can find the power of lenses in any medium.

Their are some limitations in lens maker formula that are given below,

1. The lens should be thin because the separation between the two refracting surfaces will also be small. 
2. The medium on either side of the lens should be the same. 

Power of combination of lenses 

• The power of the combination of a lens can be defined when more than one lens is used together; it is called the power of the combination of the lens. It is a simple algebraic sum of all the lenses. The formula for this is-

          Power of combination of lens = power of lens 1 + power of lens 2…                                                          P = P1 + P2

Consider two lenses, lens A and lens B with their respective focal lengths, f1 and f2. Lens A forms an image of the object at the E1 point where E1 acts as the object of lens B. The final image is produced at point E. 

PO is u, object distance for lens A 

PE is v, final image distance            

PE1 is v1 that is the image distance for lens A and object distance for lens B. 

By using lens formula on the image formed by lens A 

           1/v1 – 1/u = 1/f1……equation 1

By using lens formula on the image formed by lens B 

             1/v – 1/v1 = 1/f2…..equation 2 

By adding both the equations one and two we get, 

              1/v– 1/u= 1/f1 + 1/f2  

For the final image, 1/v – 1/u = 1/F …..Equation 3 

By equation 3 we get, 1/F = 1/f1 + 1/f2 

And we know that P = 1/F 

So, P = P1 +P2 

Where, P1 is the power of lens A and P2 is the power of lens B. 

Conclusion

Now we come to the end of the article and therefore we conclude that the power of the lens is always inversely proportional to its focal length. In simple words, a shorter focal length gives high power to the lens. So if one wants to use high power lenses, then they should prefer the lens which has a shorter focal length. We see that a lens is a transparent medium bounded by two surfaces, and one of them must be curved. And a lens can focus light to form an image, but a prism cannot. We come across terms like lens formula, lens maker formula, focal length formula and power of lens formula with their properties. Mirror and magnification equations are also applied to lenses.