2a. The types and properties of lenses

How do lenses collect light and form images?   What is a convex lens?  What is a concave lens?   What is the focal length of a lens?   How can you measure the focal length of a convex lens?

• Be able to explain how to measure the focal length of a converging lens using a distant object (see Ray diagram 2 below).

• You should revise any investigations on the behaviour of converging lenses, including real and virtual images.

• Lenses are usually made of glass, and form images by refracting the rays of light that pass through them.

  • The characteristics of the image formed depends on the shape of the lens.

  • There are two main types of lens with quite different shapes and have opposite effects when rays of light strike them.

    • They are:

    •  Convex lenses converge light rays to form an image (convex lens image ray diagram below),

    • The faces of a convex lens curve outwards so it bulges towards it centre.

      • (A fine purple line = normal at 90^o to the lens surface at that point)

      • The initial part of the rays are drawn parallel to the central axis prior to entering the convex lens..

  • 

  • 1a Simple ray diagram for a converging convex lens.

  • For a convex lens, parallel rays are brought to focus at F, the principal focus (on the other side of the lens from the object).

  • The distance from the centre of the convex lens to F is called the focal length.

    • The thinner the convex lens, the longer its focal the length - smaller angles of refraction.

    • The thicker the convex lens, the shorter the focal the length - greater angles of refraction.

    • In terms of diagrams, the AXIS of a lens is an imaginary horizontal line that passes through the centre of the lens, perpendicular to the lens, a light ray travelling along this line passes through undeviated.

  • Note the refraction effects at both air/glass boundaries of the convex lens combine to produce the converging effect - look carefully at the fine purple lines of the normals.

  • The image produced is real, meaning it can be projected onto a screen or any other surface.

  • Concave lenses diverge light rays to form an image (concave lens image ray diagram below),

    • The faces of concave lens curve inwards, narrowing the lens towards its centre - the point of the central axis.

  • 

    • 1b A simple ray diagram for a diverging concave lens

    • For a concave lens, parallel rays are brought to focus at F, the principal focus (on the same side of the lens as the object).

    • The initial part of the rays are drawn parallel to the central axis prior to entering the concave lens..

    • Note the dotted lines, extrapolated back, to indicate where you perceive the object to be - in other words, where the light appears to come from.

    • The distance from the centre of the concave lens to F is called the focal length.

    • Note again, in terms of diagrams, the AXIS of a lens is a horizontal line that passes through the centre of the lens, perpendicular to the lens.

    • Note the refraction effects at both air/glass boundaries of the concave lens to produce the diverging effect - look carefully at the fine purple lines of the normals.

    • The image produced is virtual, meaning it cannot be projected onto a screen or any other surface.

• Ray diagram 1 (below): Conventions in light ray diagrams for the two types of lenses - convex or concave.

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  • 1c representations of convex and concave lenses

  • The ray line that goes through the centre of the lens at 90^o to its surface is called the axis.

  • Note the simple representations of a convex and concave lens <------->  and >-------<

  • F is the abbreviation for focal length.

    • 2F simply means twice the focal length 2 x F.

    • Focal length f is defined as the distance from the principal focus point to the centre of the lens - explained in Ray diagram 2 below.

  • Depending on the type of lens and the position of the object the images can be

    • upright (right way up) or inverted (upside down),

    • smaller than the object, same size as object or bigger than the object (magnified),

    • the image can be real - formed when the rays directly come together after lens refraction from a convex lens (never from a concave lens),

    • or the image can be virtual - when the light rays from the object appear to come from a different place than where they originate - here you are dealing with virtual rays.

      • Concave lenses always produce a virtual image and a convex lens can under particular circumstances (see later).

      • A convex lens usually produce a real image, but can give a virtual image under specific circumstances.

    • The above 'reference' points, and in particular, understanding the differences between real and virtual images, can only be really appreciated by studying the examples of ray diagrams below.

• Ray diagram 2 (below): Ray diagram to show how to measure the focal length of a convex lens.

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• 2. converging convex lens

  • Here, refraction in a convex lens causes the rays to be converged beyond the lens.

  • The parallel set of rays are effectively from an object an infinite distance from the convex lens.

  • As already pointed out, after refraction, a convex lens brings a set of rays parallel to the principal axis to converge to the principal focus point (F on ray diagram 2 above).

  • The distance from the centre of the lens to the principal focus F is called the focal length (f) of that lens and it applies to both sides of the lens - see later convex lens forming a virtual image.

  • With a set of parallel rays the image is formed at distance F on the right of the lens and any ray passing through the centre of the lens is considered to be undeviated - not refracted.

    • These comments on what happens to the rays are really important when constructing and drawing ray diagrams.

    • Along the line of the principal axis, the thicker the convex lens (the more curved), the shorter the focal length f and the greater the magnifying power of the lens.

    • The thicker the lens (the more curved), the greater the distortion in trying to produce a well focussed image.

      • The focussing power of materials varies.

        • (It is to do with the refractive index of a material - NOT in GCSE/IGCSE physics syllabuses?).

      • However, with a more refracting material you can make the lens thinner to improve the quality of the image and keep the same magnifying power (same focal length).

  • Unless you have an optical set-up to produce a parallel beam of light from an object, you will have to resort to a much simpler method to get an approximate value of the focal length of a convex lens e.g.

  • To measure the focal length of a convex lens

    • You set up a lens to focus on a distant object - perhaps out of the laboratory window.

    • Focus the image on a screen and measure the distance from the centre of the lens to the centre of the image.

    • You can repeat the experiments with lenses of different thickness - any difference?

    • You should find the thicker the lens, the shorter the focal length.

A simple experiment using a magnifying glass to focus the Sun's rays onto a paper screen

The rays from the very distant Sun are effectively parallel and can be brought to a focus to such an extent that the converging visible light rays (and some infrared) producing such a concentration of light energy that the paper heats up sufficiently to cause charring and even ignite the paper - note the burn marks.

2b. A quick comparison of the features and characteristics of convex and concave lenses

• Comparing convex and concave lenses

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  • representations of convex and concave lenses

  • They are obviously of different shape with very different effects.

  • Convex converges light rays and concave lenses diverge rays.

  • In contrast to convex lenses, there is little variation in the image produced by a concave lens - virtual, upright and smaller than the object and on the same side as the object.

  • Depending on the position of the object, a convex lens can produce both real and virtual images, both upright and inverted images, and images can be either side of the lens and of any size - quite a variety.

• Be able to construct ray diagrams to show the formation of images by converging and diverging lenses.

  • See the index sections 3. to 8.

  • You may be asked to complete ray diagrams drawn on graph paper.

  • Know that the magnification produced by a lens is calculated using the equation:

  • magnification = image height / object height

• Know that the power of a lens is given by:

  • P = 1 / f

  • P is power in dioptres, D

  • f is focal length in metres, m

  • You should know that the power of a converging lens is positive and the power of a diverging lens is negative.

• The focal length of a lens is determined by:

  • (i) the refractive index of the material from which the lens is made

  • (ii) the curvature of the two surfaces of the lens.