Lens
Light, Sound and Waves

The eye

for 14-16

The eye is a remarkably complex optical instrument. Brain and eye work together across a huge range of light intensity, forming images of near and distant objects. These experiments explore the optics of the eye and corrective lenses.

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Model eye demonstration with flask

Lens
Light, Sound and Waves

Model eye demonstration with flask

Practical Activity for 14-16

Demonstration

A flask and lenses are used to show short and long sight and their correction.

Apparatus and Materials

  • 4-litre flat-bottomed flask and lenses with powers + 10D, + 8D and + 5D, to make a model eye (see technical notes) OR round-bottomed flask standing on a cork ring
  • + 3D and - 3D ‘correcting’ lenses
  • Light source, compact (100 W 12 V)
  • Power supply for light source, variable voltage, capable of supplying 8 A
  • Lens holder
  • Retort stand and boss
  • Slotted base
  • Thick card with central 50 mm hole
  • Plasticine
  • Fluorescein solution

Health & Safety and Technical Notes

Be aware that compact light sources using tungsten-halogen bulbs without filters are significant sources of UV. Ensure that no-one can look directly at the bulb.

Read our standard health & safety guidance


A model eye kit is available from some suppliers, e.g. Griffin Education or ASCOL.

Alternatively, the model can be constructed from three convex lenses and a flat bottomed flask filled with water as follows.

Convex meniscus lenses are preferable. Suitable 60 mm diameter meniscus lenses can be obtained from Knight Optical UK Ltd.

The lens powers have been calculated to fit a 4-litre flat-bottomed Pyrex boiling flask, whose diameter will be about 210 mm. A suitable flask (catalogue number 1070/32D) is obtainable from the supplier: Barloworld Scientific.

The flask filled with water will not be a strong enough eye by itself. For a normal eye viewing an object in front of the flask, a glass lens of power + 8D must be fixed to the front of the flask with Plasticine. A lens of + 5D is needed, instead of the + 8D, for the long-sighted eye model. A lens of + 10D is needed for the short-sighted model. Attach the three lenses, side by side, along the horizontal equator of the flask. Twisting the flask by its vertical neck will bring one lens after another into play. The lenses should be meniscus lenses so that they fit snugly on the flask.

The lenses must be chosen to combine with a suitable object distance (about 25 cm) and the size of the flask, to form an image exactly at the back of the flask. The two spectacle lenses for correction must be chosen to fit those other choices. In this case, the spectacle lens for correcting the short-sighted eye is one with power – 2D, the lens for the long-sighted eye + 3D.

The compact light source will ideally consist of a 12 V, 100 W tungsten halogen lamp in a suitable housing.

Fluorescein does not dissolve easily. Dissolve it first in a little alcohol, then dilute with water.

Fluorescein is best used in concentrations between 5 x 10 -4 g/litre and 5 x 10 -3 g/litre. These are most easily obtained by dissolving 1 g of fluorescein in 1 litre of water to make a stock solution. Between 0.5 ml and 5 ml of this stock solution is then used to each litre of water. Lower concentrations give very good contrast between the light and dark parts of the water. Higher concentrations give brighter rays and are probably better for long-distance viewing.

If fluorescein is not available, a few drops of milk will show up the beam by scattering the light.

If you don't have a compact light source (quartz iodine lamp) use a 48 W 12 V lamp.

A darkened laboratory is needed.

Procedure

  1. Fix the lenses to the flask before the lesson and fill it with very dilute fluorescein solution. The dilution of the fluorescein must be such that the whole path of the rays in the flask is clearly visible.
  2. Place the flask on a support if needed.
  3. Set up the compact light source as the object to be viewed. Support the card with the hole in it, vertically in front of the flask so that the hole is level with the lenses and serves as an iris. Rotate the flask until the + 8D lens is behind the hole and arrange the light source to lie level with the hole and the centre of the flask. Move the light source until a sharp image of it is formed on the surface of the flask. (You may prefer to put a small piece of wet paper on the back surface of the flask to make the image on that retina easily visible.)
  4. Keep the light source fixed and rotate the flask to bring first one, then the other of the two extra lenses behind the hole to show long sight and short sight. Show that the - 2D lens corrects the short-sighted eye, and the + 3D lens the long-sighted eye.
  5. Remove the correcting lenses and show what the short-sighted eye and the long-sighted eye can see in focus. Turn the flask to make a short-sighted eye, and move the light source until its image is formed on the back of the flask. Show students that the light source has to be much closer to the eye: it is a 'short-sighted' eye. Similarly show that the 'long-sighted' eye sees objects further from the eye clearly.

Teaching Notes

  • This is a very clear model of the optical properties of the eye. The cones of light show up clearly, as long as only a pinch of fluorescein is put into the flask, and the flask is rinsed out afterwards. Take care not to let water dribble down the outside of the flask between the lenses and the flask, otherwise the focus will change.
  • More able students may be able to calculate the power of lenses needed to correct sight defects before they are demonstrated.
  • The approach to calculating the prescription for spectacles is through the use of the power of the lens and the power for object and image distances.
  • For short sight: An adult has the average range of accommodation of 4D but is short sighted. Suppose she can see things comfortably if they are anywhere between 10 cm and 16.7 cm from her eye. Her accommodation therefore covers a range of 'power' from 1/0.10m-1 to 1/0.167m-1, that is from +10D to +6D, the usual 4D range for her age.
  • She should wear spectacles that form an image of a distant mountain at her far point, 16.7 cm in front of her eyes. The mountain must be moved optically from infinity (real object) to 16.7 cm (virtual image). The farthest object that her eyes can focus sends fans of rays of power 1/0.167 or 6D. With her spectacles on she wants to look at the mountain at infinity, which sends fans of rays of power 1/infinity or 0D. Therefore, 6D + spectacles must equal 0D. She needs spectacles of power -6D.
  • She can still keep her spectacles on to read a book if she wishes. Fans of rays from the book held at 25 cm have a power of 4D. Her eyes at their strongest can focus a fan of rays of power 1/0.10 m-1 or 10D. With her spectacles she can just focus a fan of power 10D + (-6D) or 4D.
  • For long sight: A student with a near point of 50 cm wishes to be able to read a book at 25 cm. He needs spectacles that will give him a virtual image of the book at 50 cm distance. His eyes alone can focus a fan of rays of power 2D but the book sends a fan of 4D. Therefore he needs lenses of +2D to help him.
  • Spectacle wearers would prefer not to have their spectacles change the magnification, so spectacles are placed approximately at the principle focus of their eyes. The combination produces a retinal picture the same size as that without spectacles but a sharp one. This is not obvious; the algebra for two separated lenses (cornea, eye lens and spectacle lens) is needed to verify it.
  • If a school has a dissectible model eye, it could profitably be shown at this stage, though it is not essential.
  • Various parts might be pointed out and named: cornea, aqueous humour, iris and ciliary muscle, crystalline lens, vitreous humour, retina and blind spot. There should be no attempt to make students learn these technical names.

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Model eye with a goldfish bowl

Lens
Light, Sound and Waves

Model eye with a goldfish bowl

Practical Activity for 14-16

Demonstration

Simulating long and short sight using a bowl and lens.

Apparatus and Materials

  • Goldfish or flower bowl
  • Large convex lens
  • Compact light source
  • Retort stand and boss
  • Fluorescein solution
  • Spectacle lenses

Health & Safety and Technical Notes

Be aware that compact light sources using tungsten-halogen bulbs without filters are significant sources of UV. Ensure that no-one can look directly at the bulb.

Read our standard health & safety guidance


The lens should have a focal length of 50 mm or less, and should be as large as possible to fit in the bowl. The maximum diameter lens commonly available at this focal length is 50 mm. This is rather small for the demonstration. A longer focal length lens could be used in a larger bowl if it can be obtained. The lens should be fixed in a hole in a disc of wood or metal and attached to a supporting rod with thread. Suitable bowls can be obtained from the supplier: Rainbow Florist Supplies.

Lenses in a wide range of powers and sizes can be obtained from the suppliers: Laser2000 or Knight Optical UK.

NB: This is a less-accurate model of the cause of eye defects than the:

Model eye demonstration with flask


Procedure

  1. Fill the bowl with water and add a little fluorescein. Hang the strong glass lens in the water by thread from a pencil placed across the top of the bowl. Use the compact source as the source of light. Focus an image on the back of the bowl by moving the lens forward and back inside the bowl.
  2. To simulate long or short sight, move the lens forward or back so that the image is now produced in front of (short sight) or behind (long sight) the rear face of the bowl. To correct this, hold the appropriate spectacle lens outside the bowl.

Teaching Notes

  • If a school has a dissectible model eye, it could profitably be shown at this stage, though it is not essential.
  • Various parts might be pointed out and named: cornea, aqueous humour, iris and ciliary muscle, crystalline lens, vitreous humour, retina and blind spot. There should be no attempt to make students learn these technical names.

This experiment was safety-tested in January 2007

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Retinal shadow

Lens
Light, Sound and Waves

Retinal shadow

Practical Activity for 14-16

Demonstration

A demonstration to show the inversion of an image on the retina, and a model to show how the shadow forms.

Apparatus and Materials

  • Thin card, small piece
  • Pin
  • Lens (+7 D)
  • Lens holder
  • White Screen
  • Lamp with compact filament
  • Retort stand and boss

Health & Safety and Technical Notes

The risk from the point of the pin is minimized if it is pushed into a small cork or bung.

Good discipline is essential so that arms are not jogged.

If students are looking towards a bright sky, ensure that this part of the sky does not contain the Sun. Otherwise, it may be impossible to prevent a student looking at the Sun through a lens.

Read our standard health & safety guidance


For part 1, the most suitable background is to use the bright sky, viewed from indoors. The effect is difficult to see if the observer is also outdoors. An alternative can be a large area of highly illuminated white surface such as the globe of a large electric light or a translucent screen very brightly illuminated from behind.

For part 2, the lamp needs to be an extended source in the vertical plane but compact in the horizontal plane. A lamp can be used if it can be suitably positioned, since its filament is vertical. With a sufficiently weak lens and a large enough distance, the shadow will be clear.

Procedure

  1. Make a large pinhole, about 1 mm diameter, in the piece of card. Hold the card 3 or 4 centimetres in front of your eye, and face the bright sky or a large illuminated surface such as the white shade of a large electric lamp. The pinhole makes a round, bright patch in the field of view. Hold the point of the pin firmly between thumb and finger (so that the point cannot possibly prick your face), and move the head of the pin up until it is between the pinhole and your eye, very close to your eye, almost among your eyelashes. You can see a shadow of the pin's head in the bright patch. The shadow is upside down.
  2. Place the lamp in front of the lens and the white screen behind the lens somewhere near the principal focus, (anywhere between 0.8f and l.5f). Position the lamp about the same distance, or less, in front of the lens. The lens does not form an image of the lamp filament on the screen but makes a round illuminated patch on it. (This patch is formed by rays going to or from an image of the filament at a much greater distance. The patch is round because the aperture of the lens is round.) You might tell students that:
  3. "The lens is not strong enough to make the rays from the filament converge to a sharp image as close as the screen."
  4. Bring a finger in - just in front of the lens, very close to it - to represent the pin's head in part 1. A shadow of the finger can be seen in the patch of light on the screen, the same way up as the finger itself.

Teaching Notes

  • This is an experiment with a surprising result. Even though the student is aware of which way up the pin is, what is seen by the brain is an inverted image.
  • The experiment leads to the conclusion that the retinal image is inverted. Students will find the argument by which this conclusion is reached difficult and puzzling until they have seen the working of a model eye. However, it is useful to do the experiment before they see a model.
  • The shadow appears inverted because with an object so close to the eye, refraction is unable to form an inverted image on the retina, so that there is only a fuzzy upright shadow of the pin on the retina. (The actual image of the pin is nowhere near the retina - it is a virtual image far away in front of the eye.) The brain interprets this upright shadow as a case of the eye seeing an object of that shape but the other way up. This inversion is the brain's natural interpretation of images on the retina, coming from one's learning in early childhood to associate retinal images with objects which can be touched. There is no question of some strange crossing over of nerves, as students sometimes think. We have never known it to be any different.
  • Students will know that if the finger and screen were object and retina for a model of an eye looking at something in focus, the image on the screen would be upside down. This can be shown by moving the lamp farther away (several focal lengths from lens) and placing a finger close to the lamp. The screen can be moved to catch the real image of the finger, now inverted.
  • Students will find it difficult to believe that the retinal shadow of a very close object is upright before the brain picks up the signals from the retina and inverts the image. The experiment shows that the shadow of a close object is indeed the same way up as the object.
  • There is a story of a scientist, Professor Cannon, who wore lenses so that the world appeared upside down to him and he had to relearn how to interpret the world around him. When he removed the lenses he found that he had learnt the lesson well and the world appeared upside down. He had to relearn all over again!

This experiment was safety-tested in January 2007

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Retinal shadow using a model eye

Lens
Light, Sound and Waves

Retinal shadow using a model eye

Practical Activity for 14-16

Demonstration

Using a model eye to show the retinal shadow created by an object close to the eye.

Apparatus and Materials

  • Model eye as used in the experiment Model eye demonstration with flask
  • Light source, compact (100 W 12 V)
  • Power supply for light source, variable voltage, capable of supplying 8 A
  • Retort stand
  • Retort stand base
  • Slotted base
  • Large card with 45 mm hole (for iris)
  • Fluorescein solution, beaker of

Health & Safety and Technical Notes

Be aware that compact light sources using tungsten-halogen bulbs without filters are significant sources of UV. Ensure that no-one can look directly at the bulb.

Read our standard health & safety guidance


Procedure

  1. Set up the model eye as in the experiment:

    Model eye demonstration with flask


  2. Place a piece of wet paper on the back of the model. Turn the flask so that the normal eye is in use. Move the lamp up close - 100 mm from the front of the flask. The lamp will make a round patch of light on the back of the flask.
  3. Hold a finger, upright, just in front of the flask and ask students to look at its shadow.

Teaching Notes

  • The lamp now represents the bright pinhole close to one's eye used in:

    Retinal shadow


  • A finger held upright just in front of the cornea lens will produce an image the same way up as the finger on an illuminated patch at the back of the flask. So, optically, the image on the retina is upright, but the image of the pin produced close to the eye is upside down. This is because of the way the brain handles the signals. It has learnt to invert the signal.

This experiment was safety-tested in January 2007

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The range of accommodation of the eye

Lens
Light, Sound and Waves

The range of accommodation of the eye

Practical Activity for 14-16

Class practical

Estimating the near point and far point for the human eye.

Apparatus and Materials

None required.

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Ask students to look out through an open window (preferably not through a pane of glass) and decide whether they can see things that are far away very sharply. If they can, they can say that their eyes see things as far as 'infinity'.
  2. Students with spectacles may wish to take them off. If they find they cannot see things very far away, they should find the farthest distance at which they can see an object comfortably and clearly by looking at objects at various distances.
  3. Now each student should look at a book held at arm's length, and bring it closer and closer to the head until the print can no longer be seen comfortably and clearly. With young eyes the range of accommodation is very large, and many students will be able to focus sharply on objects only a few centimetres from their eyes. This will involve uncomfortable squinting, which can be avoided by holding a hand over one eye.
  4. Tell students that older people do not have such a large range. They cannot see a printed page clearly when it is held so close. Holding a book so close may also be uncomfortable for their arms, is likely to be poorly lighted, and ordinary printed type will look very large. Books are printed with type that will look a comfortable size when held about 25 cm away; and at that distance the reader's arms are comfortable and the lighting can be arranged fairly easily. An 'average eye' likes to have things 25 cm away, or farther, for comfortable vision.
  5. Ask students to look at a book, read a few words, and then to look quickly at a far wall and then back at the book. It may be possible to feel the eye lens being squeezed and let go.

Teaching Notes

  • Young people have a tremendous range of accommodation. It will be confusing to attempt to persuade them that 25 centimetres is the closest distance of comfortable vision as is normally quoted. Accept the actual range each student finds. The range of accommodation for a class will vary, especially for those students who normally wear spectacles, and for the old teacher.
  • The graph shows the range of accommodation of a human eye, plotted against age. The range is in dioptres, reciprocal metres (metre -1 ). People of a given age differ widely in the placing of their near point, but their range [l/ (near distance) - (l/ (far point distance)] is much the same for most of them.
  • At age 40 the range is about 4 D. So we may think of an average eye as belonging to a person of age 40 with a near point at 25 cm and a far point at infinity. Another 40-year old whose near and far points are different can bring their range to that of an average eye with a single pair of spectacles.
  • Spectacles are designed to form virtual images so that they effectively move the object to a comfortable image point and then the eye looks at the image. Spectacles add just the right amount of lens power to the wearer's eyes to make the combination of spectacle plus eye, equal to an average eye.

This experiment was safety-tested in January 2007

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Variable focus eye

Lens
Light, Sound and Waves

Variable focus eye

Practical Activity for 14-16

Demonstration

A model eye that demonstrates how accommodation occurs.

Apparatus and Materials

  • Variable focus eye
  • Lamp, holder and stand with comb slits and cylindrical lens
  • Power supply for lamp

Health & Safety and Technical Notes

The model eye is obtainable from the supplier ASCOL, catalogue number P33-0450, Variable Focus Model Eye.

The jelly for the eye can be made by warming together, not boiling:

  • 13 parts glycerine
  • 10 parts water
  • 3 parts gelatine
  • 2 parts cane sugar (all by volume)

There are a number of variable focus eyes on the market which demonstrate accommodation. Other models have hollow plastic lenses which water can be forced into to change the curvature. Calculations can easily be carried out using this model. It has been developed from cheap lenses for use in developing countries.

Procedure

  1. The model incorporates a lens and multiple slit. Adjust the position of the lamp so that the ray streaks fall on the retina of the eye. Using the screw, vary the curvature of the lens and observe the effect.
  2. Put the lamp as close as possible to the eye so that an image is formed on the retina with the lens as fat as possible. Move the lamp farther away, and show how the curvature has to be decreased to bring the streaks to a focus on the retina.

Teaching Notes

The curvature of the lens is changed by tightening or releasing the screws. Care should be taken when explaining this, as the ciliary muscles contract all around the lens to make the eye lens fatter. A normal eye looking at infinity has relaxed muscles.

This experiment was safety-tested in January 2007

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How does the world look without glasses?

Lens
Light, Sound and Waves

How does the world look without glasses?

Practical Activity for 14-16

Demonstration

Mimicking the behaviour of short and long sight and its correction.

Apparatus and Materials

For each student

  • Spherical - 7D lens, 2
  • Spherical + 7D lens, 2

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. To demonstrate short sight you might say to students:
  2. "Hold the + 7D lenses in front of your eyes (in front of your spectacles if you usually wear them). Look at the view through the window. That is what a short-sighted person sees. Now add spectacles to correct your temporary short sight. Do this by holding – 7D lenses in front of the lenses you are already holding."
  3. To demonstrate long sight you might say:
  4. "Hold – 7D lenses in front of your eyes. Try to read a newspaper or book. Add spectacles to correct your temporary long sight. These should be + 7D lenses, held in front of the others."

Teaching Notes

  • The 'average-eye' range is from infinity to 25 cm or, in terms of power of the incident fan of rays, from 0 to 4D. The extra + 7 D lens brings that range in closer so that it runs from (0 + 7) D to (4 + 7) D or from 7D to 11D. These modified eyes are short-sighted with range from 14 cm to 9 cm.
  • To imitate long sight, the modifying lenses must be negative - the opposite of a real long-sighted person's correcting spectacles. If the student holds negative lenses in front of their eyes (or their own glasses) they will push this range outward.
  • The choice of power for those negative lenses depends on the pupil's own range, and therefore on their age. At age 14 the range will be much greater than the 4 D 'average-eye' range from 25 cm to infinity. We want the modifying lens to push the pupil's near point out beyond a usual reading distance, say to 50 cm.
  • The student who understands the idea of this quick experiment may say that the easiest way is to borrow someone else's spectacles and hold them in front. If those spectacles are for short sight you will see what a person with long sight sees. If they are for longsight you will see what a person with short sight sees.

This experiment was safety-tested in January 2007

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Teaching ray optics

Reflection
Light Sound and Waves

Teaching ray optics

Teaching Guidance for 14-16

At introductory level, simple experiments can help students to realize that light travels in straight lines and that an object is seen when light from the object enters the eye. A lens bends light rays so that the rays pass through an image point and we think we see the object at that point.

Treated as open-ended experiments they show students the way in which light behaves with real lenses in optical instruments.

Photograph courtesty of Jim Jardine

Most of the experiments described on this website are suitable for intermediate level courses. After completing them, students should be able to draw a diagram of light rays (not formal ray construction diagrams) showing the following.

  • Rays travel out from an object point in all directions, going fainter as they go farther.
  • All rays from a remote object point pass through an image point.
  • Rays from a remote object point which pass through a lens and proceed to a real image point after the lens, continue straight on through that point.
  • Rays from an object point which pass through a lens forming a virtual image emerge along lines that appear to come straight from the image point.
  • Every ray aimed at a central point in a lens (called the optical centre) passes through undeviated.

The real behaviour of rays falls short of the ideal of passing through images exactly. Students will see this and learn a little about correcting for that aberration.

The ray optics equipment suggested in these experiments looks simple, but some practical skill is needed to get the best out of it. Teaching notes provided with each experiment will help you ask the right questions of students struggling to get results.

You will be better prepared for student questions if you try out the experiments carefully beforehand. It is also advisable to read traditional textbooks that go beyond what students need to know for examination purposes. For example, knowing that the minimum distance between object and image is four times the focal length of a converging lens will enable a teacher to choose a lens that suits the length of a demonstration bench.

A well-organized cafeteria of equipment, under teacher control, will encourage students to do their own experimenting. In this way, extension work for faster students can be encouraged.

At intermediate and advanced level, ripple tanks can be brought in when needed, to show reflection or refraction for example. Wave theory predicts that all parts of a wavefront starting from a small light source arrive in phase at the image. This requires all paths from the object to take the same time.

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Dissectible model eye

Formation of Images
Light Sound and Waves

Dissectible model eye

Teaching Guidance for 14-16

A model eye and a sectional drawing of the human eye are useful to show students, and links with the biology department can usefully be made when you are teaching how cameras work.

The eye and the camera have a lot, structurally, in common.

  • The eye pupil is just a hole which lets the light in.
  • The iris is an adjustable diaphragm which controls the amount of light allowed into the eye.
  • The retina is a fine network of nerves which are sensitive to light. Most of the adjustment of the eye, between bright sunlight and complete darkness, is done by changes to the sensitivity in the retina so that the range in sensitivity may vary over a million times by storing up light sensitive chemicals for use in low light levels.
  • A camera is painted black inside; so is the eye, to lessen trouble due to stray light being reflected.
  • Most cameras have a flat film or CCD plate at the back. Some cheap ones hold the film on a curved back to allow for curvature of the image field of their simple lens. The eye has a curved back.

The camera lens must be moved in and out to focus the image of objects at different distances. The eye changes the power of its crystalline lens system by means of ciliary muscles which change the curvature of the lens. The power of an eye differs from one person to another. In round terms, the bending of the cornea is about 40D and the total power may be 60D or more.

The most important thing about the lens is that it can be squeezed to change its power. In an average eye the lens can increase by 4D when it is pulled into greater power to focus something nearby. That change for focusing objects at different distances is called accommodation.

Bear in mind that eyes do not have air in them. The materials inside an eye differ from one another in refractive index. The aqueous humour between the cornea and the lens is salty water that carries chemicals to nourish the cornea. It also presses the cornea outwards to keep it fully rounded. The vitreous humour is a less dense, clear, watery jelly which helps to keep the eyeball fully rounded.

The main refraction of light by the eye is at the front surface, the cornea, hence the success of contact lenses. Since most astigmatism is due to unequal curvature of the cornea, a spherical contact lens can remove astigmatism.

Three parts of the retina are worthy of note;

  • There is an interesting patch on the retina where all the nerves of the retina are bundled together into the optic nerve to go to the brain. There are no nerve endings there so it is a blind spot. That gives no trouble in seeing because our eyes scan all the time so you never notice your eye missing anything which falls on the blind spot for an instant. It is easy to show that the blind spot is really there by staring fixedly at X with their right eye, closing the left eye...
  • ...while bringing the page nearer. The spot disappears when its image falls on the blind spot. The blind spot is some way from the yellow spot for best seeing(see 3, below.)
  • The retina is fed by blood vessels which are just in front of the nerves so that light forming an image goes through them before reaching the nerves. Some people observe a difference in colour due to that red filter when they lie on one side on a sunlit lawn and compare the hues they see with the upper and lower eyes.
  • The human eye has a small patch of retina where there are no blood vessels in front. That is the patch used for accurate seeing, as in reading, and is called the fovea or yellow spot. You can learn about the size of it by staring at a book with one eye open and the other closed and estimate the longest word which can be read without moving the book or your eye. However, the eye has a power of 60D or so, the real yellow spot is less than the length of the word. It is at least 20 times smaller and probably less still as it is difficult to keep your eye still when looking at the word. Measurements show it is less than a 1/4 mm wide.

A cheap, fixed-focus camera has such a small aperture that, even if an object is out of focus, the cone of rays from the lens to each image point is so narrow that it makes only a small blur patch if the film catches it too soon or too late. The eye pupil closes down in bright sunlight, thus giving some depth of field. In an emergency, a person who has lost his or her spectacles can read the telephone directory by putting a card with a pinhole in front of the eye and moving closer to the page.

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