Lens Formula

Lens formula

Introduction

A lens is a transmissive optical device that can focus or disperse a light beam using refraction. A simple lens consists of a transparent material. There are two main types of lens: convex lens and concave lens. We will learn about them in detail. Glasses or plastics make lenses, and they are polished or moulded in the required shape. A lens can focus light to form an image, but a prism cannot. The lens is used in telescopes, binoculars and cameras. Lenses are also used in visual aids glasses to correct defects of vision such as myopia and hypermetropia.

Lens 

• It is a transparent medium bounded by two surfaces, and one of them must be curved. The lens is thin if the gap between two surfaces is small, and a lens will be converging with the positive focal length and diverging when the focal length is negative. 
• The assumptions made of the lens are that the lens is thin. Therefore, the lens has small apertures, the object lies close to the principal axis, and the incident ray makes a small angle with the surface of the lens or the principal axis. 
• A lens can focus light to form an image, but a prism cannot. The lens is used in telescopes, binoculars and cameras. Lenses are also used in visual aids glasses to correct defects of vision such as myopia and hypermetropia. 
• Devices that focus or disperse waves and radiation other than the visible light are also called lenses, such as microwave, electron, acoustic, or explosive. there are two commonly known types of lenses:

Concave lens

• The concave lens is defined as a lens formed by combining two spherical surfaces together in such a way that they are curved inwards. 
• The focal length of the concave lens is negative.
• This lens is also called diverging lens because it diverges the light rays falling on them.  
• In this lens, edges are thicker than in the middle.
• Examples of concave lenses are cameras, binoculars, telescopes, and eyeglasses which are used to correct nearsightedness.

Convex lens

• The convex lens is defined as a lens formed by combining two spherical surfaces together in such a way that they are curved outwards.
• The focal length of the convex lens is positive.
• This lens is also called a converging lens because it converges the light falling on them.
• The middle part of the lens is thicker than the edges
• Examples of the convex lens are the human eye, magnifying glass, eyeglasses which are used to correct farsightedness or hyperopia, microscopes, projector, and multi-junction solar cells.

Lens formula

The lens formula is the relationship between the distance of the image, the distance of an object, and the focal length of the lens. It can be written as –

                                1/v – 1/u = 1/f

Where v = distance of an image 

              u = distance of an object

              f = focal length.

Lens maker formula

• The lens maker formula can be defined as the relation between the lens’s focal length to the refractive index of the material and radii of curvature of the two surfaces.
•  It is used to make the lenses of a particular power from the glass of a given refractive index.
• The lens maker formula is-

          1/f = (n-1) x (1/R1 – 1/R2)

Where f = focal length of a lens 

              n = refractive index

              R1 and R2 = the radius of curvature of both surfaces.

Focal length formula

• The focal length can be defined as how strong the lens converges or diverges light. 
• A positive focal length tells that a lens converges the light.
• A negative focal length tells that a lens diverges the light.
• A lens with a shorter focal length bends the rays more sharply.
• Focal length is the inverse of the optical power of the lens.

Where f = focal length

              R = radius of curvature of the given lens.

• The typical focal length formula is-

    1/f = 1/v – 1/u 

Where, f = focal length

              u = image distance

              v = object distance.

Power of lens formula

• The power of the lens formula can be defined as the reciprocal of its focal length.
• The formula is-

                          D =1/f 

Where D = it is the power in diopters.

               f = focal length in metres.

• dioptre D is the SI unit of the power lens.
• The power of the concave lens is negative. Because it is a diverging lens. 
• The power of the convex lens is positive. Because it is a converging lens. 
• 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

Magnification

The magnification of a lens is defined as the ratio of the height of the image to the object. And it is denoted as m.

   m = height of the image/ height of the object.

m = hi/ho

Where hi is the height of the image and ho is the height of the object.

Magnification in terms of u and v 

Magnification is equal to the ratio of image distance to object distance.

                                m = v/u

where, v = image distance from the lens.

             u = object distance from the lens.

Magnification by convex lens

• A convex lens forms virtual and real images. And the magnification produced by this lens is either positive or negative. 
• Positive Magnification = virtual image
• Negative Magnification = real image
• When,

          |m| > 1, – magnified image

          |m| < 1, – diminished image

          |m| = 1, – image size is equal to the object size

Magnification by a concave lens

• Concave lenses form virtual images only. And the magnification produced by this lens is always positive.
• The image formed by a concave lens is always smaller than the object.

So, 

       |m| < 1

Conclusion

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. Lenses are also used in visual aids glasses to correct defects of vision such as myopia and hypermetropia. We also see two types of lenses: concave lenses, which are diverging lenses. A convex lens is also called a converging lens. 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. But the mirror equation is known as the lens maker formula when we deal with lenses.