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# Focal Length of a Convex Lens Using u-v Method

A convex lens has a positive focal length. The focal length of the lens at a particular point is the distance between the point and the center of curvature of the lens.

An optical device which is used to diverge or converge Rays is known as lens. There are two types of lens: convex lens and concave lens.  A type of lens which is used to diverge the beam of Light which incident on it is known as diverging lens or concave lens. This lens helps to create a virtual image on the opposite side of the reflecting surface. Images formed by concave lenses are virtual, erect and diminished.  We use concave lenses to correct eye disease known as myopia (nearsightedness). It helps to focus the beam of light on the retina by diverging the light before they get focused on the eye lens.

On the other hand, the lens which converges light incident on it is known as converging lens or convex lens. These lenses converge the incident Ray towards the principal axis. Convex lens is used to correct hypermetropia (farsightedness).  This lens reflects the beam of light before it enters the eye and hence, decreases the distance of image formed. Image formed by a convex lens is real, inverted and smaller in size than the object when the object is placed at focus.  Other applications of convex lenses are used in projectors, cameras, simple telescopes, magnifying glass etc. Now we are going to learn more about convex lenses in order to find the focal length of a convex lens by various methods.

## Focal Length of a Convex Lens

The distance between the lens and its focus is known as the focal length of a lens. The focal length of the convex lens is the measure of how sharply it converges the light.

For convex lens or converging lens, the focal length is always positive.

It is denoted by f.

### Important Terms Used in the Experiment to Find Focal Length of a Convex Lens

Centre of Curvature:  It is the centre of the sphere from which the lens has been cut. It is denoted by C.  Lens has two Centre of curvature as they are formed by the combination of two parts of spheres.

Radius of Curvature:  The radius of curvature is the distance from the vertex to the centre of curvature.

Principal Axis: It is the line passing through both the curvatures of the lens.

Principal Focus: Principal focus of a convex lens is a point on the principal axis where the light-ray converges after reflection.

## Properties of Convex Lens

It is thicker in the middle and thinner at the edges.

It is known as the converging lens as the light Ray passes through the lens tends to meet at a point.

The image formed by a convex lens is real. Hence, it can be obtained on screen.

Focal length of a convex lens is denoted by f which is the difference between optical centre of the lens and the principal Focus.

The image would be real, inverted and smaller in size if it is formed at the focus of the lens.  The refracted Ray converges on the other side of the convex lens.

## Lens Formula

The relationship between the focal length image distance and object distance is given by the formula known as the lens formula. This formula is applicable for both lenses concave as well as convex.

1/f = 1/v + 1/u

### How to Find Focal Length of a Convex Lens?

Aim:  To find the focal length of a convex lens using u-v method

Material required:  a convex lens with lens holder, screen, optical bench, illuminated object.

Process to find focal length of a convex mirror using u-v

To find the focal length of a convex lens it is necessary to have the value of v and u. i.e. the distance between the object and the lens and the distance between the image and lens.

• Place the object on the optical bench in such a way that lens should lie in between the screen and the object.
• Now adjust the position of the lens and the screen until we obtain a sharp image of an object on the screen.
• When you obtain a sharp image of an object measure v and u. The distance from lens to object will give you “u” and distance from lens to image will give you “v”.
• Now we can easily calculate the focal length of convex lens by using formula,

f = uv/ v+u

The focal length of a convex lens is calculated using the lens formula,

1/f = 1/v + 1/u

u -is the distance between the object and the lens

v -is the distance between the image and the lens

f -is the focal length of the lens

1/f = v+u/uv

f = uv/ v+u

note: in the case of virtual images we put negative signs.

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### Conclusion

In this module we have learned about lens- a device which diverges or converges the beam of light. There are two types of lens: concave lens and convex lens. Concave lens is a diverging lens whereas convex lens is a converging lens. Convex lens is used to correct the eye disorder known as hypermetropia whereas concave lens is used to correct myopia. Focal length is a measure of how strongly the lens or mirror converges or diverges a light. We can find the focal length of a lens by using the lens formula.

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