Converging Lenses (Leaving Cert Physics): Revision Notes

Converging Lenses

Introduction

A converging lens, also known as a convex lens, is thicker at the centre than at the edges. When parallel light rays pass through a converging lens, they bend inward and meet at a point called the focal point. Understanding how these lenses form images is crucial for explaining many optical devices we use every day, from cameras to magnifying glasses.

How images are formed in converging lenses

When light from an object passes through a converging lens, each point on the object emits light rays in all directions. The lens refracts these rays, causing them to change direction as they pass through.

The key principle is that after refraction at the lens, rays from the same point on the object will either:

• Converge (meet) at a specific point to form a real image
• Appear to diverge from a point to form a virtual image

Properties of real images

A real image is formed when light rays actually intersect after passing through the lens. This type of image has several important characteristics:

Real images are commonly seen in cameras, projectors, and our eyes, where the image forms on the retina.

Image formation at different object positions

The position of an object relative to a converging lens determines the type, size, and location of the image formed. There are several key scenarios to understand:

Object beyond twice the focal length (beyond 2f)

When the object is placed at a distance greater than twice the focal length from the lens:

• A real image is formed
• The image is diminished (smaller than the object)
• The image is inverted
• The image forms between f and 2f on the opposite side

Object at twice the focal length (at 2f)

When the object is positioned exactly at twice the focal length:

• A real image is formed
• The image is the same size as the object
• The image is inverted
• The image forms at 2f on the opposite side

Object between the focal length and twice the focal length (between f and 2f)

When the object is placed between f and 2f:

• A real image is formed
• The image is magnified (larger than the object)
• The image is inverted
• The image forms beyond 2f on the opposite side

Object at the focal point (at f)

When the object is positioned exactly at the focal point:

• Light rays emerge parallel after refraction
• No image is formed (or the image is said to be at infinity)

Object inside the focal length (between lens and f)

When the object is closer to the lens than the focal point:

• A virtual image is formed
• The image is magnified
• The image is upright (right way up)
• The image appears on the same side as the object

Virtual images in converging lenses

Virtual images are formed when the refracted light rays appear to diverge from a point, even though they don't actually meet there. When you trace these diverging rays backwards, they appear to come from the image location.

The magnifying glass

A magnifying glass is a practical application of virtual image formation. When you hold a magnifying glass close to an object (placing the object inside the focal length), you see a magnified, upright, virtual image.

Images of distant objects

When observing very distant objects (effectively at infinity), the light rays arriving at the lens are essentially parallel. These parallel rays converge at the focal point of the lens, forming a real image at the focal plane.

This principle is fundamental to:

• Cameras - where distant scenes form sharp images on the sensor/film
• Telescopes - where distant stars and planets form images at the focal point
• The human eye - where the crystalline lens focuses distant objects onto the retina

The lens formula

The mathematical relationship between object distance, image distance, and focal length is given by the lens formula:

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

Where:

• f = focal length of the lens
• u = distance from object to lens (object distance)
• v = distance from lens to image (image distance)

Sign conventions

Using the formula

The lens formula allows you to:

• Calculate where an image will form when you know the object position and focal length
• Determine if an image is real or virtual from the sign of v
• Find the focal length of an unknown lens using object and image measurements

Remember!