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Lens Formula: Derivation, Magnification, Power of Lens

Lens Formula

The lens formula is given below. The Lens formula can be used to calculate the distance between the image and the lens.

1/u + 1/v = 1/f.

V = distance of the image from the lens.

U=distance of an object from the lens.

F=focal length.

The lens formula applies to all situations. If the equation results in negative image distance, then the image is virtual. If the equation shows a negative focal length then the lens is a diverging lens.

Also Read: value of root 2

Lens Formula: What is a Lens formula?

A lens is a piece of glass that either concentrate the rays of light at a point or it diverges the light from one concentrated point. It does the converging or diverging with the help of dispersion. A simple lens consists of a transparent material while the compound lens consists of several lenses.

Lenses can be broadly classified into two types. They are convex lens and concave lens. A convex lens is also known as a converging lens. The reason is when rays of light fall on the lens, the rays get converged when refracted back.

A concave lens is called a diverging lens as light rays diverge apart after falling on the lens. Images formed by the convex lens can either be real or virtual. It depends upon factors like the distance of the image from the lens and the size of the lens and the object.

The distance between the image and the lens can be calculated by the focal length and the object distance using the lens formula.

 

Lens Formula Derivation: Lens Maker Formula

Lens Formula: Derivation, Magnification, Power_40.1
Derivation of Maker Formula

Below we have pointed the derivation of the lens formula.

First surface

n2/v1 –n2/v2=n2-n1/r…………………………1

 

Second surface

N1/v –n2/v1=n1-n2/r2………………………2

Adding 1 and 2 we get,

1/v-1/u= (n2/n1-1)[1/R1-1/R2]

Also,

1/v-1/u=1/f

Hence, 1/f= (refractive index-1)(1/R1-1/R2)

Check: CSA of a cylinder formula

Lens Formula: Power of lens Derivation

  • The measure of the degree of the converging and diverging rays is known as the power of lens.
  • It will depend upon the focal length of the lens.
  • The SI unit of power is Dioptre.
  • The power of the concave lens is told to be negative and the power of the convex lens.

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Lens Formula: Example

  1. If an object is 12cm from a concave lens with a focal length of 6cm what is the image distance from the lens and is the image upright or upside down?

Solution:

=> F=do+di

=> 1-6=112+di

=> -0.166=0.0833+di

=> di=-0.25

=> 1 -0.25=di

=> di=-4

All concave images are upright.

Hence solution is −4 and Upright.

 

FAQ of Lens Formula for Class 12

What is Mirror formula and lens formula?

The lens formula is f = v-u and the mirror formula is f=v+u

How do you use lens formula?

You can use it to find the distance between the image and the lens.

What is V and U in Lens formula?

U is object distance and v is image distance in lens formula

What is the formula of convex lens?

1/u + 1/v = 1/f.

What is magnification formula?

Magnification formula represents the ratio of the height of the image to the ratio of the height of the object.

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