Lenses - CCEA

• The difference between converging and diverging lenses.

• How to draw a lens diagram.

• The application of lenses.

• Identifying defects of vision and how they are corrected using lenses.

When light moves from air into glass or plastic it is refracted, that is it changes direction due to the change in density.

Lenses are used in cameras, telescopes, binoculars, microscopes and corrective glasses.

A lens can be converging (convex) or diverging (concave).

A converging lens is thicker in the middle than it is at the edges.

Parallel light rays that enter the lens converge.

They come together at a point on the principal axis called the principal focus F, (or focal point).

The centre of the lens is called the optical centre C.

In a ray diagram, a converging lens is drawn as a vertical line with outward facing arrows to indicate the shape of the lens.

Key point

1. The focal length f of a converging lens is defined as the distance between the optical centre, C, and the principal focus, F.

2. Focal length is measured in m, cm or mm.

• Point the lens at a distance object outside the window – for instance a tree or building. The greater the distance, the better. Rays of light from this object are taken to be parallel as the object is assumed to be at infinity.

• Move the position of the screen behind the lens until a sharp image is formed on it.

• Parallel rays of light form an image at the principal focus of a lens, and so the screen is at the principal focus. The distance between the optical centre of the lens and the screen is the focal length, f.

• Measure this distance with a 30 cm rule and record in a suitable table.

• Repeat the process several times and calculate the average focal length.

A diverging lens is thinner in the middle than it is at the edges.

This causes parallel rays to diverge.

They separate but appear to come from a principal focus F on the other side of the lens.

In a ray diagram, a diverging lens is drawn as a vertical line with inward facing arrows to indicate the shape of the lens.

The images formed by a lens can be:

• upright or inverted (upside down compared to the object);

• enlarged or diminished (smaller than the object);

• real or virtual.

A real image is an image that can be projected onto a screen.

Rays of light actually pass through the image.

A virtual image cannot be projected onto a screen.

It appears to come from behind the lens and can only be seen by looking through the lens.

Rays of light appear to come from a virtual image, rather than pass through it.

Convex lenses

The type of image formed by a convex lens depends on the lens used and the distance from the object to the lens.

The magnification of lens is defined as the ratio of the height of the image to the height of the object.

M = Hᵢ / Hₒ

A magnification value greater than 1 means the image is enlarged.

A magnification value less than 1 means the image is diminished.

Cameras and eyes contain convex lenses.

For a distant object that is placed more than twice the focal length from the lens, the image is:

• between F and 2F on the opposite side of the lens to the object;

• inverted;

• diminished;

• real.

Projector

Projectors contain convex lenses.

For an object placed between one and two focal lengths from the lens, the image is:

• further away than 2F on the opposite side of the lens to the object;

• inverted;

• enlarged;

• real.

In a film or data projector, this image is formed on a screen.

Film must be loaded into the projector upside down so the projected image is the right way up.

The table below summarises the nature of the images produced by a converging lens.

The normal, human eye forms a real, diminished, inverted image on the retina.

Most of the refraction occurs at the air – cornea boundary.

Light then enters the lens after passing through the pupil.

The converging (convex) lens provides the rest of the refraction necessary to focus the rays of light sharply on the light sensitive cells of the retina at the back of the eye.

The ciliary muscles change the shape and hence the focal length of the lens, allowing the eye to focus on both near and far objects.

What is the near point?

• The closest distance from the unaided eye at which an object can be seen clearly is called the near point.

• The near point is 25cm for a normal, adult eye.

What is the far point?

• The furthest distance from the unaided eye at which an object can be seen clearly is called the far point.

• The far point is taken to be infinity for a normal, adult eye.

What is range of vision?

• The normal, adult, human, eye can see clearly objects at distances of 25cm from the eye to infinity.

• This range is more limited for the very young or as we get older.

• A long-sighted person can see objects a long distance away (they have good long sight) but can’t see objects a short distance away. A long-sighted person can read writing on a whiteboard in a classroom clearly but cannot read print in a book or newspaper sharply.

• Images of nearby objects (at 25cm from the eye) are formed behind the retina. The image is blurred.

• Long sight is due to the eyeball being too short, or the lens cannot be made thick enough by the ciliary muscles to focus the light rays on the retina. Long sight often occurs in older people as the ciliary muscles weaken with age

• Rays from a nearby object need to be converged more to form the image on the retina.

• Long sight is corrected using a converging lens which starts to converge light rays from a nearby object before they enter the eye.

• Converging (convex) lenses are used in reading glasses.

• A short-sighted person can see close objects clearly (they have good short sight), but they can’t see distant objects clearly.

• A short-sighted person can read a book clearly but cannot read writing on a whiteboard in a classroom or a car number plate at distance.

• The image of a distant object, say 2 m to 3 m from the eye, is formed just in front of the retina, causing it to appear blurred.

• This defect is due to the eyeball being too long or the ciliary muscles cannot make the lens thin enough.