## What is a Converging Lens?

Converging lens, also known as a convex lens, is thinner at the upper and lower edges and thicker at the center. The edges are curved outwards. This lens can converge a beam of parallel rays of light that is coming from outside and focus it on a point on the other side of the lens.

## Anatomy of a Convex Mirror

Principal axis: it is a horizontal straight line passing through the centre of the lens.

Optical axis or vertical axis: A vertical line passing through the centre of the curvature of a lens.

Optical centre: This is the central point of the lens where the principal and optical axis intersects.

Focus (F): It is a point on the principal axis at which the parallel rays converge.

Focal length: it is the distance between the center of the convex lens and the focal point.

### Real image

When the image formed is inverted as compared to the object, the image formed is called a real image. This type of image can be captured on a screen. A converging lens produces a real image when the object is placed at a point more than one focal length from the lens.

### Virtual image

When the image formed is upright as compared to the object, and cannot be produced on the screen, it is called a virtual image. A converging lens will produce a virtual image when the object is placed within one focal length of the lens. It produces a magnified image on the same side of the lens as the object. It acts as a magnifying glass.

## Magnification of Convex Lens

Magnification is the factor by which the image enlarges or diminishes.

m = hi ¸ h

where

• m = magnification
• hi = height of object
• ho = height of object

If the value of m is one, the size of the image and object are the same. If the value of m is greater than one, the image is enlarged. And if m is less than one, the image is diminished.

If there is a positive magnification, the image formed is virtual but if the magnification is negative the image formed is real.

## Ray Diagram

We can draw a ray diagram for a convex lens as follows

• A ray from the top of the object passing through the optical centre without a change in direction.
• A parallel ray from the top of the object till the optical axis. It then refracts to pass through the focal point on the other side of the lens.
• A ray passing through the focal point till the optical axis. It then refracts to form a ray parallel to the principal axis.

The point where these three rays intersect is where the image is formed.

However, you can obtain the position of the image by drawing any two of the three rays mentioned above. The point at which the two rays will intersect will be the top of the image. Three rays are drawn for greater accuracy of the position of the image.

The properties of the image formed depend on the placement of the object on the principal axis. The table summarises the properties:

## The Thin Convex Lens Equation

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Where

• f : the focal length
• v: the distance that lies between the image and the optical centre of the lens
• u: the distance that lies between the object and the optical centre of the lens

By convention, the convex lens has a positive focus.

## Types of Convex Lens

There are three types of the convex lens which differ in their structure.

1. Plano-convex lens

This lens is curved outwards from one side and the other side is plane. The positive focal length elements of the lens have one curvature surface and one flat surface. When used it will deliver images with less spherical distortion.  They are most commonly used when the object is far away from the lens. In optical physics, it is termed infinite conjugate. An example of the same is when you want to focus light from a faraway object like the star.

1. Double convex lens

A double convex lens, also known as a biconvex lens or just convex lens, is curved outwards at both sides of the lens. These are also used to focus light but are preferred when the object is closer to the lens. This is termed finite conjugate in optical physics. An example of the same is microscopy.

1. Concave-convex lens

Also known as the meniscus lens, the concave-convex lens has a structure where one side is curved inwards and the other side is curved outwards. This means that the surface on one side of the lens is concave and the other side’s surface is convex. This lens is used in controlling laser beams.

## Uses of Convex Mirrors

Side wing mirrors and rear-view mirrors of a car use convex mirrors. This is because the diminished image formed gives the driver a larger field of view than the normal human eye. Helps the driver have a better check on the road and traffic behind.

It is also used in driving mirrors and shop security mirrors as it gives the viewer a wider view than normal. Moreover, it serves as an advantage to view blind corners on the road – blind corner mirrors. It helps in road safety by being able to view the traffic around sharp corners.

They are used in eyeglasses. This is because convex lenses can be used for correcting farsightedness. Farsightedness occurs when the distance between the eye's lens and the retina becomes too short. As a result of which the focal point now lies behind the retina. So, the convex lens in eyeglasses increase refraction which accordingly reduces the focal point

## Guidance

• You should try remembering the table of the object positions and image properties.
• While drawing ray diagrams it is important to be precise and draw thin lines to get an accurate position of the image.
• Prefer drawing three rays on ray diagrams for accurate results.

## Similar Topics

• The concave or diverging lens
• Mirrors and lenses
• Optical physics

## Context and Application

This topic is studied in 11th, 12th standard as well as

• Bachelors in Science (Physics)
• Masters in Science (Physics)

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