OPTICS - types of lenses, ray diagrams

Doc Brown's Physics Revision Notes

Suitable for GCSE/IGCSE Physics/Science courses or their equivalent

 This page will answer many questions e.g.

 How can 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?



  • REMINDERS what happens when light rays pass through transparent rectangular or triangular prisms:

      • 1. No refraction when a light ray strikes a different medium at 90o to the surface ie 'down' the normal.

        • The same applies to 3 and 4 for the central ray in the diagram.

      • 2. Double refraction through a rectangular glass block at the air/glass interfaces, note that when the ray emerges back into air its path is parallel to the original incident ray.

      • 3. Refraction of two rays at the two surfaces of a diverging concave lens (this page).

      • 4. Refraction of two rays at two of the surfaces of a triangular glass or plastic prism.

      • 5. Refraction of two rays at the two surfaces of converging concave lens (this page).

  • 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, usually made of glass, 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 that converge light rays to form an image (below image on left and diagram 5 above),

        • a convex lens curves outwards towards its centre,

      • and a concave lenses that diverge light rays to form an image (below image on right and diagram 3 above),

        • a concave lens curves inwards towards its centre.

  • Examples of how to construct ray diagrams

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

    • representations of convex and concave lenses

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

    • 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),

      • they can be 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,

      • 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.

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

      • -

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

    • converging 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.

    • After refraction, a convex lens brings a set of rays parallel to the principal axis to converge on 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.

      • The thicker the convex lens, the shorter the focal length f.

    • 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.

    • 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?

    • -

  • Ray diagram 3 (below): Ray diagram showing the formation of an image from an object O at a distance of 2F from the lens (twice the focal length) beyond the convex lens.

    • converging lens

    • To construct the ray diagram, draw a vertical line tipped with an arrow for the object O, at the appropriate distance from the lens, in this case a distance exactly 2F from the lens.

    • Draw a ray from the arrow tip parallel to the principal axis into the lens.

    • Since this is parallel to the axis, the ray must continued down through the principal focus (in this case beyond a 2F distance to the right of the lens). Check this line in ray diagram 2 above.

    • You then draw a line, again from the top of the object, down through the centre of the lens, and continue the line until it is beyond intersecting with the first ray you drew. Again, check this line in ray diagram 2 above.

    • The intersection point gives you the position of the bottom of the image and the inverted arrow gives you the size of image I.

    • From the diagram you can see that the image I is real (formed directly by converging rays, inverted (upside down) and the same size as the object and at a distance of exactly 2F beyond the lens.

    • Above is quick sketch of how to do the ray diagram 3 on graph paper. If done very carefully to scale, you can then calculate the height of the image I and the distance from the lens to the image I.

    • -

  • Ray diagram 4 (below): The formation of a virtual image by a convex lens when the object O is a distance from the lens between F and 2F.

    • converging lens

    • You construct this ray diagram as exactly described for ray diagram 3.

    • The image is real, inverted and larger than the object.

    • The image is further than a distance 2F from the lens.

    • So here the lens is acting as a magnifying glass.

    • Above is quick sketch of how to do the ray diagram 4 on graph paper. If done very carefully to scale, you can then calculate the height of the image I and the distance from the lens to the image I.

    • -

  • Ray diagram 5 (below): The formation of a virtual image by a convex lens when the object O is between F and the lens.

    • converging lens

    • To construct this diagram, as with the others, from the top of the object you take the ray parallel to the principal axis down through the principal focus point F. That is what parallel rays do.

    • The second ray from the top of the object you take down through the centre of the lens without deviation.

    • However, in this case these rays do not intersect to give you the position of the image - they diverge, but all is not lost to get to an image!

    • Therefore you have to extrapolate back with the dotted line virtual rays until they intersect.

      • Virtual rays are where the rays from the object appear to come from, they do NOT exist in reality.

      • BUT, you can't construct the ray diagram to get to the characteristics of the image without using them!

    • This then gives you the position and size of the virtual image - this time on the same side of the lens as the object.

    • The image is virtual, right way up (erect, NOT inverted), bigger than the object (a 'magnifying glass' effect).

    • Unlike all the other situations, the (not real) virtual image is on the same side of the lens as the object and beyond the object.

      •  In this case the image is between the distances F and 2F to the left of the lens.

    • The thickness of the lens affects its magnifying power - the thicker the lens, the more powerful the magnifying glass.

    • Above is quick sketch of how to do the ray diagram 5 on graph paper. If done very carefully to scale, you can then calculate the height of the image I and the distance from the lens to the image I.

    • -

  • Ray diagram 6 When the object O is beyond a distance of 2F from the lens

    • converging lens

    • If the object is a long way from the lens the image is formed between F and 2F.

    • The image is real inverted (upside down!) and smaller than the object.

    • If the object is at infinity, the focussed image is at a distance F from the lens.

    • This means the further the object O is from the lens, the nearer the image I is to distance F.

    • This is also the image formed in a telescope from a very distant object like a star which is so far away that the incoming rays are effectively parallel.

      • The image can then be magnified by another lens or lenses in conjunction with an eyepiece.

    • Above is quick sketch of how to do the ray diagram 6 on graph paper. If done very carefully to scale, you can then calculate the height of the image I and the distance from the lens to the image I.

    • -

  • If the object is a F, the image is at infinity, which is not very useful? (not needed for GCSE physics?).

    • Graph paper ray diagram to show how an image is formed at infinity.

    • -

  • Ray diagram 7a showing the rays diverging when passing through a concave lens

    • diverging lens

    • Here, refraction in a concave lens causes the rays to be diverged - spread out beyond the lens.

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

    • Starting with a set of rays parallel to the principal axis, diverge them based on the point F the principal focus.

    • Then, when you extrapolate back from the divergent rays, all the dotted lines intersect at the principal focus point F.

    • The dotted lines are virtual rays (where the rays from the object appear to come from),

      • and all the virtual rays meet up at a single point F.

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

    • I emphasise that these dotted lines are called virtual rays because they indicate where the light rays from the object appear to come from - these dotted rays do NOT exist - its not reality!

    • -

  • Ray diagram 7 The formation of an image O by a concave lens.

    • diverging lens

    • The ray from the top of the object is taken down through the centre of the lens undeviated.

    • You then take the ray parallel to the principal focus and diverge it in line with the principal focus F - that's how parallel rays behave.

    • You then extrapolate back with a dotted line (virtual ray) to the principal focal point F.

    • Where the two lines intersect gives you the top of the image and hence its size too.

    • A concave lens always produces a virtual image, the right way up, smaller than the object and is situated somewhere between the object and the lens (i.e. on same side as object).

      • These image characteristics are independent of the position of the image - can be anywhere!

    • Above is quick sketch of how to do the ray diagram 7 on graph paper. If done very carefully to scale, you can then calculate the height of the image I and the distance from the lens to the image I.

    • -

  • Comparing convex and concave lenses

    • representations of convex and concave lenses

    • They are obviously of different shape - 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.

    • -

 


Practicals you may have done

Revise any investigations on the use of converging lenses to:

(a) measure the focal length using a distant object

(b) investigate factors which affect the magnification of a converging lens (formulae are not needed)

(c) explain how the eyepiece of a simple telescope magnifies the image of a distant object produced by the objective lens (ray diagrams are not necessary).


Eye structure and function and correcting eye defects will be on another page


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Waves - electromagnetic radiation, sound, optics-lenses, light and astronomy revision notes index

General introduction to the types and properties of waves and how to do wave calculations, ripple tank experiments

Illuminated & self-luminous objects, reflection of visible light, ray box experiments, ray diagrams explained, uses of mirrors

Refraction and diffraction, the visible light spectrum, prism investigations, ray diagrams explained

Electromagnetic radiation, sources, types, properties, uses and dangers

The absorption and emission of radiation by materials - temperature & surface factors

See also Global warming, climate change, reducing our carbon footprint from fossil fuel burning

Optics - types of lenses (convex and concave), experiments and ray diagrams

The visible spectrum of colour, light filters and explaining the colour of objects

Sound waves - properties explained, uses of sound including ultrasound, earthquake waves

See also more detailed notes on The Structure of the Earth and earthquake waves (seismic waves)

The electromagnetic spectrum and astronomy - solar system, cosmology, nuclear fusion and the life cycle of stars

The Big Bang Theory of the Universe, the red-shift and microwave background radiation


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