NOTE the spelling of a single 'lens' - it has no 'e' on the end!

Lenses are used to focus light. They do this by refraction.

You need to know the names of two types of lens and the way that they refract three parallel rays of light.

In the above diagram the refraction of the rays is shown at BOTH lens surfaces.

In the diagram below a SYMBOL for the lens is used - showing the refraction at each surface is then not necessary... it is shown happening at a 'line' - in exam questions make sure you carefully look to see whether symbol or lens drawing is required.

A convex lens close to the object (a distance less than the focal length) give a virtual, erect, enlarged image - it works as a magnifying glass.

A convex lens at an infinite distance from an object produces a real (can be picked up on a screen), inverted image. This fact is used in the camera to photograph distant objects.

In the above diagram the refraction of the rays is shown at BOTH lens surfaces.

In the diagram below a SYMBOL for the lens is used - showing the refraction at each surface is then not necessary... it is shown happening at a 'line' - in exam questions make sure you carefully look to see whether symbol or lens drawing is required.

The pole of the lens is the centre of the lens. Rays drawn passing through this point are not diverted, they continue in a straight line.

The focal length of a lens is the distance between the pole of the lens and the focal point OR the perpendicular distance between the axis of the lens and tha focal plane..

The focal point or principal focus of a convex lens is point through which rays of light travelling near to and parallel to the principal axis pass after refraction by the lens. (The point all emerging rays pass through).

The focal point or principal focus of a concave lens is point fromwhich rays of light travelling near to and parallel to the principal axis seem to emerge from after refraction by the lens. (The point all emerging rayscan be 'traced back' through).

Click here to go to the page on how to construct rays through lenses

Lens diagrams give a visual representation of the image formation but the formula makes up for any imperfections in your drawing skills!.  It gives an accurate calculation of the position of the image - the sign giving you an indication of whether it is real or virtual. A positive sign indicates a real image (formed on the opposite side of the lens from the object) and vice versa. 

A length measurement should strictly be done in metres. If it is not you will have to think carefully about the units of any related physical quantity found from a formula using that length.

It does not matter if you work in cm or mm with this equation, as long as you are consistent. 

However if you are going to find the power of the lens in dioptres you must work out the focal length in metres first.

A convex lens has a real focus - therefore the power of a convex lens is a positive value. If you are longsighted the optomotrist will prescribe you a lens with a positive power value.

A concave lens has a virtual focus - therefore the power of a concave lens is a negative value. If you are shortsighted the optomotrist will prescribe you a lens with a negative power value.

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The magnification of a lens is the ratio of the size of the image to the size of the object (how many times bigger the image is than the object was!). If the ratio is greater than one the image is bigger than the object (enlarged) and if it is less than one it is smaller than the object (diminished in size).

We can relate object and image size to similar triangles:

We therefore get a simple equation to work with:

Since v is in metres, and u is in metres, M has no units.

See also the refracting telescope

and the camera

Correction of Sight Defects - see the eye