OPTICS - types of lenses, ray diagrams

Doc Brown's Physics Revision Notes

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

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 'bulging' 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, narrowing 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 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).

• 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 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.

• (Its do with the refractive index of a material - NOT in GCSE physics syllabus).

• 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.

• 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 convex 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.

• A ray passing through the centre of a lens is considered NOT to be deviated - NOT refracted.

• Please remember this applies to ANY lens, and, for convex lenses only, a ray parallel to the principal axis, after refraction, passes through the principal focus point F, when studying the rest of the diagrams on this page.

• 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 convex 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 beyond 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 convex lens - here the convex lens is acting as a magnifying glass.

• 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.

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

• This is the ray diagram for a convex lens acting as a magnifying glass.

• You should know the magnification formula:

• magnification = size of image  ÷  size of object

• e.g. if the image was 20 mm high and the object was 4 mm high

• magnification = 20 ? 4 = 5 (no units, but remember the two sizes must be in the same units!)

• 2nd example of calculation

• Suppose the magnifying power of a lens is 3.0.

• If an object is 2.0 cm high, calculate the size of the image.

• Rearranging the magnification formula:

• size of image = magnification x size of object

• size of image = 3.0 x 2.0 = 6.0 cm

• -

• Ray diagram 6 When the object O is beyond a distance of 2F from the convex 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 7b 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 object - it can be anywhere!

• Reminder: A virtual image cannot be projected onto a screen.

• 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 defects and their correction

The eye contains a convex lens that, ideally, focuses the incoming light rays to produce a sharp image on the retina at the back of the eyeball. The light receptors in the retina then transmit the electrical signals to the brain giving you vision. However, the eye does not always sharp images, but it is possible to correct these defects using glass lenses.

See also The eye - structure, function and vision defects GCSE biology revision notes - This page deals with all the GCSE biology required on the eye and more notes on other methods of dealing with eye defects.

Cause of vision defects

A malfunction of the eye in some way to give blurred vision because the incoming light rays do not form a sharp image on the retina.

1. Causes of short-sightedness (the medical term for short sightedness is myopia)

Short sighted people can't focus correctly on distant objects.

There are many 'biological' causes to make a person short-sighted, but here we are most concerned with optics of the situation and how to use concave lenses to correct the defect.

The eyeball can be too long so the image is formed in front of the retina.

Distant objects will seem blurred, though close objects may be in focus.

The same effect is caused if the lens is the wrong shape i.e. it is too powerful - too thick - with too short a principal focus, so your vision is blurred.

This can be corrected with a diverging concave lens (see the diagrams and explanation below).

2. Causes of longsightedness (the medical term for long sightedness hyperopia)

Long sighted people can't focus correctly on near objects.

There are many 'biological' causes to make a person long-sighted, but here we are most concerned with optics of the situation and how to use convex lenses to correct the defect.

The eyeball may be too short so the image is formed behind the retina.

Distant objects might be in focus but any relatively close objects will appear blurred.

The same effect is caused if the lens is the wrong shape - too weak - too thin - with too long a principal focus, so your vision is blurred.

This can be corrected with a converging convex lens (see the diagrams and explanation below).

Using lenses to correct for eye defects

1. Correcting for short-sightedness

Reminder: Short sighted people can't focus correctly on distant objects.

The eyeball is too long or the lens to thick (too strong) to produce a sharp image on the retina.

Prior to correction, the focussed image is formed in front of the retina.

In order to move the image back to give it a sharp focus on the retina you need to diverge the rays. This is done with a diverging concave lens in front of the eye.

The diverged rays are then brought to a focus further back by the eye lens onto the retina.

The diagrams (1) show the normal correct function of the eye, the effect of short-sightedness and the correction produced by the concave lens.

2. Correcting for longsightedness

Reminder: Long sighted people can't focus correctly on near objects.

The eyeball is too short or the lens to thin (too weak) to produce a sharp image on the retina.

Prior to correction, the image is formed behind the retina.

In order to form a sharp image on the retina, you to use a converging convex lens in front of the eye to bring the rays to a focus further forward.

The combined converging power of the glass lens plus the eye lens bring the rays to a focus on the retina on the inner surface of the eyeball.

The diagrams (2) show the normal correct function of the eye, the effect of long-sightedness and the correction produced by the convex lens.

See also The eye - structure, function and vision defects GCSE biology revision notes - This page deals with all the GCSE biology required on the eye and more notes on other methods of dealing with eye defects.

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