L5 & 6 - Lenses

objectives

Core

• Describe the action of a thin converging lens on a beam of light
• Use the terms principal focus and focal length
• Draw ray diagrams for the formation of a real image by a single lens
• Describe the nature of an image using the terms enlarged/same size/diminished and upright/inverted.

Extended

• Describe the difference between a real and virtual image
• Use and describe the use of a single lens as a magnifying glass

Types of Lens

• Concave lenses These are thin in the middle and thickest round the edge. When rays parallel to the principal axis pass through a concave lens, they are bent outwards.
• The principal focus is the point from which the rays appear to diverge (spread out). A concave lens is a diverging lens.

How Lenses Bend Light

Real images formed by convex lenses

• In the diagram below, rays from a very distant object are being brought to a focus by a convex lens. Rays come from all points on the object. However, for simplicity, only a few rays from one point have been shown. Together, the rays form an image which can be picked up on a screen. An image like this is called a real image. It is formed in the focal plane.
• In a camera, a convex lens is used as below to form a real image on a piece of film or CCD. The image in the eye is formed in the same way.

Real images formed by convex lenses

• The rays from a point on a very distant object are effectively parallel, so the image passes through the principal focus. However, for an object at any other distance, the image is in a different position.
• You can predict where a convex lens will form an image by drawing a ray diagram. There are two examples next. Each has these features:
  • For simplicity, rays are drawn from just one point on the object.
  • The rays used are standard rays. These are chosen because it is easy to work out where they go. Only two of them are needed to find where the image is.
  • For simplicity rays are shown bending at the line through the middle of the lens. In reality, bending takes place at each surface.

The ray diagrams above show that as the object is moved towards the lens, the image becomes bigger and further away. A film projector uses a convex lens to form a magnified, real image on a screen a long way away from it, as in the lower diagram.

Convex Lens as a Magnifying Glass

• If an object is closer to a convex lens than the principal focus, the rays never converge. Instead, they appear to come from a position behind the lens. The image is upright and magnified. It is called a virtual image because no rays actually meet to form it and it cannot be picked up on a screen. Used like this a convex lens is often called a magnifying glass.

Drawing accurate ray diagrams

Problems like the one below can be solved by doing a ray diagram as an accurate scale drawing on graph paper:

• An object 2 cm high stands on the principal axis at a distance of 9 cm from a convex lens. If the focal length of the lens is 6 cm, what is the image's position, height, and type?

For accuracy, you need to choose a scale that makes the diagram as large as possible. In the drawing below, 1 cm on the paper represents 2 cm of actual distance. When the final measurements are scaled up, they show that the image is 18 cm from the lens, 4 cm high, and real.

Estimating the focal length of a convex lens

• You can find an approximate value for the focal length of a convex lens by forming an image of a distant window (or other distant bright object) on a screen. Rays from the window are almost parallel, so the image is close to the principal focus of the lens. Therefore the distance from the image to the lens is approximately the same as the focal length.

Convex lenses in a telescope

• The telescope above (shown without its tube) uses two convex lenses. The objective forms a real image of a distant object in this case the Moon - just inside the principal focus of the eyepiece. The image acts as a close object to this lens, which forms a magnified virtual image of it.
• The eyepiece is being used as a magnifying glass, but it is magnifying an image of the object rather than the object itself. The final image is upside down. Most binoculars - two telescopes side-by-side - have prisms in them to turn the image the right way up

Images formed by concave lenses

In the diagram below, two standard rays have been used to show how a concave lens forms an image. Wherever the object is positioned, the image is always small, upright, and virtual.

Applications of Lenses - Cameras

• This uses a convex lens to form a small, inverted, real image on a sensor (or in older cameras, a piece of photographic film) at the back.
• The image sensor is a light-sensitive microchip containing millions of microscopic solar cells. When the shutter opens, these capture the image as a pattern of electric charge which can be stored as data on a memory card.
• This can be processed to produce the final image on a screen or in print.

Convex Lens Essentials

Real image An image formed by rays that converge. It can be picked up on a screen. Focus Any point where rays leaving a lens converge. If the rays entering the lens are parallel to its axis, then they converge at the principal focus (F on one side of the lens, F' on the other). Rays from a point on a very distant object are effectively parallel.

The Human Eye

• Like a camera, this uses a convex lens system to form a small, inverted, real image at the back. The light is mainly converged by the cornea and the watery liquid behind it. The lens, which is flexible, is used to make focusing adjustments: its shape is changed by a ring of muscles.
• The image is formed on the retina, which contains over 100 million light-sensitive cells. Signals from these cells are sent to the brain along the optic nerve.

The Projector

The projector above uses a convex lens, called the projection lens, to form a large, inverted, real image on a screen. The object is a tiny, brightly lit, picture on an LCD (liquid crystal display) panel rather like the one on a mobile phone. (In older systems, the picture is on a piece of film.)

For the projected image to be upright, the picture on the panel must be upside-down. For a large image, the panel has to be just outside of the principal focus of the projection lens, and the lens a long way from the screen. To make focusing adjustments, the lens is moved backwards or forwards slightly.