The **Power of the Lens** is a fundamental concept in optics that deals with the ** ability of a lens to bend light.** The

**which are the standard units of measurement in science.**

*power of a lens is expressed in SI units,*The power of a lens and understanding its definition, calculation, and formula is essential for students studying the optics chapter in Class 10.

The topic **Power of Lens** is not only important for **Class 10 students**, but it is also vital for those preparing for various government exams such as SSC, CDS, UPSC, RRB NTPC, or other state-level exams.

This topic falls under the **general science category,** making it a significant aspect for those pursuing a career in government jobs. Having a sound understanding of this concept can be beneficial for these aspirants in their exam preparation and increase their chances of success.

## What is Lens?

▪ Lenses are optical components that are **made of transparent glass and have curved surfaces.**

▪ Their **primary function** is to **refract light and control its path,** resulting in the creation of** magnified or dispersed images.**

▪ They are used in a wide range of devices, such as **telescopes, cameras, and magnifying glasses, to enhance the quality of the images.**

▪ In cameras, **multiple lenses **are** used to gather light **and** create a clear and sharp image.**

▪ The **magnification of a lens is determined by the relationship between the size of the object and the size of the resulting image.**

▪ By combining multiple lenses, the blurriness, and distortion caused by a single lens can be reduced, leading to a more defined image.

▪ The definition of the power of a lens states that it is **the reciprocal of the focal length of a lens,** and it is **expressed in diopters (D).**

## Power of a Lens

▪ The concept of the power of a lens is an interesting topic in the field of Ray Optics. It **refers to the ability of a lens to bend light, **which is crucial for its refraction properties.

▪ The power of a lens determines its capacity to converge or diverge light, with **convex lenses having a converging ability and concave lenses having a diverging ability.**

▪ It is important to note that the power of a lens is closely related to its focal length. A **shorter focal length** means that the **lens can bend light more effectively,** resulting in a **higher power**. Conversely, a** longer focal length results in lower power.**

▪ It is important to understand that the **power of a lens and its focal length have an inverse relationship.** As the focal length decreases, the power of the lens increases, and vice versa. A **lens with a short focal length is therefore said to have high optical strength.**

Also see, List of optical instruments with examples

## Focus and Focal Length of a Lens

▪ **Lenses are optical components** that are made of **transparent materials, such as glass**, and are **used to manipulate the path of light.** They do this by taking advantage of the** property of refraction**, which is the **bending of light as it travels from one medium to another**.

▪ When light passes through a lens, it **either converges or diverges, **forming an image. Lenses are widely used in various devices such as magnifying glasses, **Microscopes, eyeglasses, signal lights, contact lenses, projection condensers, viewfinders, and on simple box cameras.**

▪ The focal length of a lens is a **measure of how effectively it focuses or disperses light. **It is **inversely proportional to the optical power of the lens,** with a **shorter focal length indicating a higher power.**

▪ The **focal length is defined as the distance from the center of the lens (the pole) to the focal point,** which is the point where the light converges after passing through the lens from infinity. This distance is** represented by the letter “f.”**

▪ It’s important to note that the **focal length of a spherical lens can be either positive or negative,** depending on the location of the focal point.

▪ **Positive focal lengths** **indicate** that the **focal point is located on the same side of the lens** as the incoming light, while **negative focal lengths indicate** that the **focal point is located on the opposite side.**

### Positive Focal length

▪ The focal length of a lens determines whether it is a converging lens or a diverging lens. If the **focal point of the lens is located on the side of the lens opposite to the object**, it is said to have a** positive focal length**, which is an indicator of convergence.

▪ This is **commonly seen in convex lenses**, where parallel light beams entering the lens parallel to its principal axis converge at a single point referred to as the real focus.

### Negative Focal Length

▪ On the other hand, if the **focal point of the lens is located on the side of the object,** it is said to have a **negative focal length,** which indicates divergence.

▪ This is usually **observed in concave lenses,** where parallel light beams entering the lens appear to diverge from a virtual focus.

▪ Hence, a **positive focal length shows convergence,** whereas a **negative focal length indicates divergence.**

▪ The shorter the focal length of a lens, the more sharply the light is bent, leading to quicker convergence or divergence. This makes lenses with short focal lengths ideal for applications that require a stronger magnifying or dispersing effect.

## Power of a Lens Formula

▪The calculation of the power of a lens involves the use of a formula. The formula for the power of a lens is given by:

P = 1 / f

- where “f” is the focal length of the lens, expressed in meters.

▪ It is important to note that a positive power indicates that the lens is converging, and a negative power indicates that the lens is diverging.

▪ The greater the power of a lens, the more strongly it will bend light.

▪ This means that a lens with a high power can form a clear, sharp image from a distant object, while a lens with a low power will produce a blurry image.

### SI Unit of Power of Lens (for Class 10)

▪ The **S.I. Unit of power is a Dioptre**. It is **denoted by the letter ‘D’.**

▪ So, The power of the lens is **calculated in Diopters (D)** if the **focal length **is given in** meters**.

▪ When f = 1 meter, P = 1/ f = 1/ 1 = 1 dioptre.

Hence, 1 dioptre is the power of a lens whose focal length is 1 meter.

▪ The power of a lens is measured by an instrument called dioptre meter.

### Examples of SI Unit of Power of Lens

▪ The formula for calculating the power of a lens in dioptres is given by:

P = 1/f,

where “f” is the focal length of the lens in meters and “P” is the power in dioptres.

So, a lens with a focal length of 1 meter has a power of 1 dioptre, while a lens with a focal length of 0.5 meters has a power of 2 dioptres. (P= 1/0.5, or P = 10/5, or P =2, 2D )

### Define 1 Dioptre of Power of Lens (Class 10)

▪ Now, We know that the unit of measurement for the power of a lens is the dioptre (D). **One dioptre of power** is defined as the **ability of a lens to refract light i**n such a way that** it converges **to a** focus one meter away from the lens. **

▪ In other words, a** lens with a power of 1 dioptre** will form an image that is **one meter away from the lens** and has the same size as the object being imaged.

### Dioptre Formula

▪ The formula to calculate the optical power of a lens or curved mirror is expressed as:

D = 1/f

▪ Where, **D is the power of the lens** or **curved mirror in diopters**, and **f is the focal length** of the lens or curved mirror **in meters.**

▪ In other words, the **dioptre is a unit used to quantify the refractive power of a lens,** and the dioptre formula provides a way to calculate this power by taking the reciprocal of the lens’s focal length in meters.

▪ ThePower of a combination of lensespower of a combination of lensesis calculated byadding the powers of each individual lens.▪ Whentwo or more lenses are placed together, their individual powers combine to produce a single equivalent power.▪ The formula for the equivalent power of a combination of lenses is given by i.e. P = P1 + P2 + P3 + ……… Where P = power of combination of lenses. P1, P2, P3, ……………… = Powers of individual lens placed close to each other.

## Numerical Example

▪ The focal length of a lens is 25 cm. Calculate the power of that lens. Write the type of this lens.

**Solution:**

Given, Focal length, f= 25 cm

Lens Power Formula, P = 1/f

So, P= 1 / 0.25 (0.25 m = 25 cm )

Or, P = 100/25

Or, P= 4

Oe, P=4D

Since the focal length is +ve, so, the lens is convex

## Summary

▪ In summary, lenses play a key role in optics due to their ability to control light and create clear magnified images. They are commonly used in various applications and devices, and the use of multiple lenses helps to enhance the quality of the final image.

▪ The power of a lens **Formula P=1/f (Focus)**▪ The SI unit of Power of the lens is Diptre, denoted by D.

▪ The power of a combination of lenses is calculated **by adding the powers of each individual lens. **

▪ Power of a Convex lens is positive (As focal length +ve)

▪ Power of a Concave lens is negative (As focal length -ve)

## Frequently Asked Questions (FAQs)

### Q1. What is the formula for the power of a lens?

Answer: P (Power)= 1/f (Focal Length), P is the power in diopters and f is the focal length in metres.

### Q2. What is the power of a convex lens?

Answer: The power of a Convex Lens is positive. (as its focal length is positive)

### Q3. What is the power of a concave lens?

Answer: The power of a Concave Lens is negative. (as its focal length is negative)

### Q4. What is the SI unit of power of lens?

Answer: The SI unit of power of the lens is Diopter.