If a halogen gas is introduced into the bulb to create a tungsten halogen lamp, the filament can be operated at higher temperature to give greater efficacy (up to 25 lm/W). This causes more evaporation of tungsten from the filament, but this combines with the halogen and is redeposited on the filament, rather than on the inside of the glass, leading to increased bulb life. If of high wattage, the envelope is made of fused silica or quartz and can deteriorate if touched with the fingers when oil or moisture can be transferred. Low wattage versions use aluminophosphate glass, but problems of uneven heating and subsequent failure can still occur if the glass envelope is touched.

While you are undoubtedly aware of liquid crystal displays (LCDs) found in watches, calculators, computer screens, cellphones, flat screen televisions, and other myriad places, you may not be aware that they are based on polarization. Liquid crystals are so named because their molecules can be aligned even though they are in a liquid. Liquid crystals have the property that they can rotate the polarization of light passing through them by 90º. Furthermore, this property can be turned off by the application of a voltage, as illustrated in Figure 12. It is possible to manipulate this characteristic quickly and in small well-defined regions to create the contrast patterns we see in so many LCD devices.

As well as the rod and cone photoreceptors, the retina contains intrinsically photosensitive retinal ganglion cells (ipRGC) which contain a photopigment called melanopsin. This has a peak absorption around 470 nm, and the ipRGC are part of the signalling pathway which sets the body clock to its 24-hour cycle (circadian rhythm). The exposure to ‘daylight’—intense blue light especially in the morning—increases the production of melatonin towards the evening time, and this causes sleepiness. Some visually impaired individuals with retinal disease may have an abnormality in the circadian system because their ipRGC are also affected, and they experience sleep disturbance, which can have further consequences for physical and mental health. However, some individuals with total vision loss can have a normal sleep-wake cycle because their circadian receptors are preserved ( ). To try to reduce sleep disturbance, individuals should have exposure to high light levels (and preferably natural daylight) during the early part of the day. If they need a light to be on continuously at night (in case they need to get out of bed), this should be a red/amber light to avoid stimulating the ipRGC. Melatonin tablets are sometimes prescribed to be taken at night, to regulate the sleep-wake cycle.

The illuminance on surfaces within a room also depends on the décor. If walls and ceiling are pale, they have high reflectance, then a specific light source creates a greater task illuminance than if the surroundings were dark. If light from a luminaire is directed towards the ceiling, then the ceiling must be light in order to reflect that light into the room.

Tubular fluorescent lamps could also be described as low pressure mercury discharge lamps. An electrical discharge passed through the mercury gas causes its atoms to lose electrons (become ionised) which collide with other atoms. These collisions cause further ionisation, or the absorption of energy with the result that some electrons are raised to a higher energy state. As these fall back, the energy is emitted in the form of visible and ultraviolet (UV) radiation. The latter is absorbed by the phosphor coating on the inside of the envelope and re-emitted in the form of visible radiation. The radiation emitted from the mercury is at certain discrete wavelengths, but the spectral composition can be broadened by careful choice of these phosphors. Because the output of short-wavelength light is increased over that produced by incandescent lamps, some people consider fluorescent lighting to be too ‘cold’ for household use. These lamps have an efficacy of at least 40 to 60 lm/W, thus using about one-quarter the power to achieve the same luminous flx compared to incandescent lamps. They also require much less frequent replacement. Some control circuitry is required to limit the electrical current through the lamp, and this can add to the physical size and weight of the installation. Compact fluorescent lamps are available where the long discharge tube is folded or bent into a circular or spiral configuration. The circular tube can be arranged around the large diameter lens in a variable-focus stand magnifier. Limiting the size using the spiral configuration allows it to be used as an energy-saving replacement for an incandescent filament lamp, but this is often not successful because the shade has been designed for an incandescent envelope which gives its maximum intensity straight down, whereas the fluorescent tube emits maximum intensity sideways. It takes up to 3 minutes for the older compact fluorescent lamps to reach maximum brightness from a starting brightness at switch-on of 50% of the maximum: if used for ambient lighting, especially on staircases or corridors where the occupant is passing through, this could create a hazard. The compact fluorescent is extremely successful, however, in purpose-made localised task lighting. The high efficacy means that there is little energy lost as heat, so that the lamp housing does not get as hot as would that surrounding an incandescent bulb. This means that the patient can place their head very close to the lamp without discomfort and can grasp the housing to adjust it without risking burning their hand. However, compact lamps without the covering envelope should not be used closer than 30 cm for more than 1 hour per day, due to a UV hazard.

By now you can probably guess that Polaroid sunglasses cut the glare in reflected light because that light is polarized. You can check this for yourself by holding Polaroid sunglasses in front of you and rotating them while looking at light reflected from water or glass. As you rotate the sunglasses, you will notice the light gets bright and dim, but not completely black. This implies the reflected light is partially polarized and cannot be completely blocked by a polarizing filter.

Until recently, incandescent filament lamps with their characteristic pear-shaped envelopes of soda–silica–lime glass were the most common form of household lighting. Due to their high energy use, these bulbs are no longer sold in Europe. In these bulbs, a tungsten filament is heated and an inert gas fills the envelope to help slow the evaporation of tungsten from the filament. This increases bulb life and prevents blackening of the inside of the glass (which would reduce light output). Clear glass envelopes can give harsh shadows and act as a glare source, so it is more usual to have a frosted ‘pearl’ finish to the glass to diffuse the light without significant loss of brightness. The efficacy of incandescent lamps is approximately 10 lm/W, being higher for higher wattage lamps. This is a very poor rating, with a lot of energy being wasted as heat, but the lamps are very cheap, small and compact, relatively long-lasting and require only simple electronic circuitry. Light output is biased towards longer wavelengths, and this gives a ‘warm’ light which is favoured for household use.

To examine this further, consider the transverse waves in the ropes shown in Figure 3. The oscillations in one rope are in a vertical plane and are said to be vertically polarized. Those in the other rope are in a horizontal plane and are horizontally polarized. If a vertical slit is placed on the first rope, the waves pass through. However, a vertical slit blocks the horizontally polarized waves. For EM waves, the direction of the electric field is analogous to the disturbances on the ropes.

The Sun and many other light sources produce waves that are randomly polarized (see Figure 4). Such light is said to be unpolarized because it is composed of many waves with all possible directions of polarization. Polaroid materials, invented by the founder of Polaroid Corporation, Edwin Land, act as a polarizing slit for light, allowing only polarization in one direction to pass through. Polarizing filters are composed of long molecules aligned in one direction. Thinking of the molecules as many slits, analogous to those for the oscillating ropes, we can understand why only light with a specific polarization can get through. The axis of a polarizing filter is the direction along which the filter passes the electric field of an EM wave (see Figure 5).

Figure 5. A polarizing filter has a polarization axis that acts as a slit passing through electric fields parallel to its direction. The direction of polarization of an EM wave is defined to be the direction of its electric field.

Photographs of the sky can be darkened by polarizing filters, a trick used by many photographers to make clouds brighter by contrast. Scattering from other particles, such as smoke or dust, can also polarize light. Detecting polarization in scattered EM waves can be a useful analytical tool in determining the scattering source.

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A ‘black body’ is a theoretical object which absorbs all radiation which hits its surface. It only emits light when it is heated: when heated to a specific temperature, it emits light of a particular colour, ranging from reddish white (corresponding to a low colour temperature) to blueish white (a high colour temperature). The colour temperatures typically seen in white lights range from around 2800 (red/orange—a ‘warm’ colour) to 6500 K (blue—a ‘cool’ colour).

Figure 9. Long molecules are aligned perpendicular to the axis of a polarizing filter. The component of the electric field in an EM wave perpendicular to these molecules passes through the filter, while the component parallel to the molecules is absorbed.

A fairly large angle between the direction of polarization and the filter axis is needed to reduce the intensity to 10.0% of its original value. This seems reasonable based on experimenting with polarizing films. It is interesting that, at an angle of 45º, the intensity is reduced to 50% of its original value (as you will show in this section’s Problems & Exercises). Note that 71.6º is 18.4º from reducing the intensity to zero, and that at an angle of 18.4º the intensity is reduced to 90.0% of its original value (as you will also show in Problems & Exercises), giving evidence of symmetry.

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Increasing the task illuminance cannot compensate completely for the small size and low contrast of difficult visual tasks, however, and Fig. 11.3 shows that changing the size of the task detail is more effective ( ). Thus, the larger size letters always support a better performance, even when illumination is optimised, and the performance with low-contrast targets cannot be improved to match that produced by high contrast letters (although for medium-contrast levels, it can be brought close to it). It is also clear that whilst large increases in performance can be created by improving the contrast, these are not so great as the effects achieved with increases in the letter size (compare the improvement in changing the 1.5 min arc target from a contrast of 0.56 to 0.97, and note that it is less than the improvement of increasing the size to 3 min arc, whilst maintaining 0.56 contrast). Extrapolating these findings to low vision, it can be seen that increasing the illumination is not a replacement for magnification of the image, but only a supplement to it: no matter how much the illumination is increased, it does not bring the performance of a visually demanding task (small detail, low contrast) up to the level of a visually easy task. An increase in illuminance will produce a greater improvement in performance on a near-threshold task than on a visually easy task, and the low-vision patient is much more likely to be working near to their visual threshold. Magnifiers can offer a much greater range of improvement in performance compared to lighting alone, but performance will still be limited for large letters if the illumination is suboptimal: no magnifier will produce optimum performance without sufficient light.

Figure 11. Polarization by scattering. Unpolarized light scattering from air molecules shakes their electrons perpendicular to the direction of the original ray. The scattered light therefore has a polarization perpendicular to the original direction and none parallel to the original direction.

Figure 13. Optical activity is the ability of some substances to rotate the plane of polarization of light passing through them. The rotation is detected with a polarizing filter or analyzer.

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Figure 2. An EM wave, such as light, is a transverse wave. The electric and magnetic fields are perpendicular to the direction of propagation.

Figure 8. Polarization by reflection. Unpolarized light has equal amounts of vertical and horizontal polarization. After interaction with a surface, the vertical components are preferentially absorbed or refracted, leaving the reflected light more horizontally polarized. This is akin to arrows striking on their sides bouncing off, whereas arrows striking on their tips go into the surface.

The amount of light emitted by a light source is called the luminous flx and is measured in lumens . The efficacy of a particular light source is the quantity of luminous flx which is created by a given input of electrical energy, and this is expressed in lumens per watt . This light now spreads out from the source, and the quantity of light hitting the working surface or task is described as the illuminance, which is defined as the amount of light per unit area. It is measured in lumens per square metre, which are also called lux (lx) . Consider a light source emitting a particular amount of light—luminous flx, measured in lumens—and illuminating the working area from a distance d . If the light source is moved further away from the surface, then the area it illuminates (the area over which the amount of light is spread) will increase. As the distance doubles, the area illuminated increases fourfold, and thus the illuminance decreases by a factor of 4. This represents the inverse square law: illuminance of an object is inversely proportional to the square of the distance of the light source from that object. Illuminance of the surface decreases if it is tilted, because this also increases the area to be illuminated ( Fig. 11.1 ). If the surface is tilted by an angle α (or the light source is placed at an angle α with respect to a perpendicular to the surface) the illuminance will be proportional to the cosine of angle α : this is the cosine law.

[latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex] gives [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}=\frac{1.333}{1.00}=1.333\\[/latex].

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Figure 6 shows the effect of two polarizing filters on originally unpolarized light. The first filter polarizes the light along its axis. When the axes of the first and second filters are aligned (parallel), then all of the polarized light passed by the first filter is also passed by the second. If the second polarizing filter is rotated, only the component of the light parallel to the second filter’s axis is passed. When the axes are perpendicular, no light is passed by the second.

Since the part of the light that is not reflected is refracted, the amount of polarization depends on the indices of refraction of the media involved. It can be shown that reflected light is completely polarized at a angle of reflection θb, given by [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex], where n1 is the medium in which the incident and reflected light travel and n2 is the index of refraction of the medium that forms the interface that reflects the light. This equation is known as Brewster’s law, and θb is known as Brewster’s angle, named after the 19th-century Scottish physicist who discovered them.

Figure 3. The transverse oscillations in one rope are in a vertical plane, and those in the other rope are in a horizontal plane. The first is said to be vertically polarized, and the other is said to be horizontally polarized. Vertical slits pass vertically polarized waves and block horizontally polarized waves.

Polarizing filters have a polarization axis that acts as a slit. This slit passes electromagnetic waves (often visible light) that have an electric field parallel to the axis. This is accomplished with long molecules aligned perpendicular to the axis as shown in Figure 9.

What angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce its intensity by 90.0%?

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Brewster’s law: [latex]\tan\theta_{\text{b}}=\frac{{n}_{2}}{{n}_{1}}\\[/latex], where n1 is the medium in which the incident and reflected light travel and n2 is the index of refraction of the medium that forms the interface that reflects the light

Some LEDs have the facility to tune the colour temperature to individual preference across the range from 2700 to 6500 K. On a table lamp, this may be a manual control, but ‘smartbulbs’ which can have colour temperature and brightness controlled by a smartphone app, or voice controlled via a digital assistant, are also available. The low power of LEDs means batteries last a long time in these types of magnifiers. Unlike incandescent lamps, where the light gets dimmer as the batteries lose their power, LEDs maintain their brightness over time until the batteries have not got enough power to work them and then the light stops working altogether.

Thus, the maximum illuminance is obtained by having the most intense light source, placed as close as possible to the task and perpendicular to the surface rather than obliquely: distance is the most significant factor in determining the illuminance in a given situation. The formula given only applies to the direct illumination from a point source: indirect illumination by reflection can make a significant contribution to the illuminance created by extended sources if the distance from the working plane is greater than 5× the size of the light source.

If you hold your Polaroid sunglasses in front of you and rotate them while looking at blue sky, you will see the sky get bright and dim. This is a clear indication that light scattered by air is partially polarized. Figure 11 helps illustrate how this happens. Since light is a transverse EM wave, it vibrates the electrons of air molecules perpendicular to the direction it is traveling. The electrons then radiate like small antennae. Since they are oscillating perpendicular to the direction of the light ray, they produce EM radiation that is polarized perpendicular to the direction of the ray. When viewing the light along a line perpendicular to the original ray, as in Figure 11, there can be no polarization in the scattered light parallel to the original ray, because that would require the original ray to be a longitudinal wave. Along other directions, a component of the other polarization can be projected along the line of sight, and the scattered light will only be partially polarized. Furthermore, multiple scattering can bring light to your eyes from other directions and can contain different polarizations.

When the intensity is reduced by 90.0%, it is 10.0% or 0.100 times its original value. That is, I = 0.100I0. Using this information, the equation I = I0 cos2 θ can be used to solve for the needed angle.

Figure 8 illustrates what happens when unpolarized light is reflected from a surface. Vertically polarized light is preferentially refracted at the surface, so that the reflected light is left more horizontally polarized. The reasons for this phenomenon are beyond the scope of this text, but a convenient mnemonic for remembering this is to imagine the polarization direction to be like an arrow. Vertical polarization would be like an arrow perpendicular to the surface and would be more likely to stick and not be reflected. Horizontal polarization is like an arrow bouncing on its side and would be more likely to be reflected. Sunglasses with vertical axes would then block more reflected light than unpolarized light from other sources.

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Only the component of the EM wave parallel to the axis of a filter is passed. Let us call the angle between the direction of polarization and the axis of a filter θ. If the electric field has an amplitude E, then the transmitted part of the wave has an amplitude E cos θ (see Figure 7). Since the intensity of a wave is proportional to its amplitude squared, the intensity I of the transmitted wave is related to the incident wave by I = I0 cos2 θ, where I0 is the intensity of the polarized wave before passing through the filter. (The above equation is known as Malus’s law.)

Glass and plastic become optically active when stressed; the greater the stress, the greater the effect. Optical stress analysis on complicated shapes can be performed by making plastic models of them and observing them through crossed filters, as seen in Figure 14. It is apparent that the effect depends on wavelength as well as stress. The wavelength dependence is sometimes also used for artistic purposes.

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Older people are likely to gain more benefit from improved task illuminance than the younger age group. The performance of these two groups can be equated if the illuminance is high enough, and it is suggested that the decrease in the amount of light reaching the retina is the cause of the poorer performance in the elderly subjects. There is increased absorption and scattering of light by the ocular media with advancing age, in addition to senile miosis ( ). reported a threefold decrease in the amount of light reaching the retina of a 60-year-old compared to that of a 20-year-old: describe even more dramatically the 22-fold decrease in transmission of light of wavelength 400 nm by the ocular media between the ages of 1 month and 70 years.

Thus, people performing difficult visual tasks (and a given task will always be more difficult for the low vision patient as it will be nearer to the limit of their ability) require the highest level of illumination. A further consideration of Fig. 11.2 suggests, however, that there are limits to how high this illuminance can be raised. In point (d), the performance has reached an optimum plateau for both age groups, but it may well decrease due to glare if excessive illumination is used. There is also an increase in the amount of light scatter by the ‘normal’ crystalline lens after the age of 40 years which will contribute to a loss of contrast of the retinal image, even if the object itself is of high contrast. Thus, the decreasing performance with excessive illuminance is represented by point (e), showing that the effect is likely to be more marked in the older subjects. For some low-vision patients, the plateau (c) may not be reached: performance may be affected by glare even at modest levels of illumination.

The design of the luminaire—the housing for the lamp—can be just as important as the light source itself: it controls the amount and direction of the light output as well as offering a simple physical support, the electricity supply and a means of heat dissipation for the lamp. The bare lamp envelope does not necessarily emit light in the required direction, and may also create a glare source if viewed directly, so the lamp housing can be used to control the light. This can be done by obstruction, diffusion, refraction, reflection, or any combination of these. Obstruction is used when the lamp is surrounded by an opaque material which prevents light being emitted in that direction. Light is then only emitted through a limited aperture in the shade—usually at the bottom, and sometimes at the top of a ceiling-mounted lamp in order to create diffuse reflection from the ceiling. Diffusion occurs when a translucent cover is placed over the light, increasing the spread of the light but also usually absorbing a considerable proportion of it. The lamp covering can be made in the form of multiple prismatic elements to refract the light and redirect it into the required position. Reflection of light from the inside of the luminaire is also an extremely efficient way of deflecting all the light into the required direction. At its most extreme, the reflecting surface is specially shaped and highly polished to maximise the effect (such as in car headlamps), but it is frequently used less dramatically by the inside surface of a lampshade having a matt white finish. Dirt and deterioration of the luminaire surfaces can cause light loss over time.

Light reflected at these angles could be completely blocked by a good polarizing filter held with its axis vertical. Brewster’s angle for water and air are similar to those for glass and air, so that sunglasses are equally effective for light reflected from either water or glass under similar circumstances. Light not reflected is refracted into these media. So at an incident angle equal to Brewster’s angle, the refracted light will be slightly polarized vertically. It will not be completely polarized vertically, because only a small fraction of the incident light is reflected, and so a significant amount of horizontally polarized light is refracted.

Figure 10. Artist’s conception of an electron in a long molecule oscillating parallel to the molecule. The oscillation of the electron absorbs energy and reduces the intensity of the component of the EM wave that is parallel to the molecule.

Many crystals and solutions rotate the plane of polarization of light passing through them. Such substances are said to be optically active. Examples include sugar water, insulin, and collagen (see Figure 13). In addition to depending on the type of substance, the amount and direction of rotation depends on a number of factors. Among these is the concentration of the substance, the distance the light travels through it, and the wavelength of light. Optical activity is due to the asymmetric shape of molecules in the substance, such as being helical. Measurements of the rotation of polarized light passing through substances can thus be used to measure concentrations, a standard technique for sugars. It can also give information on the shapes of molecules, such as proteins, and factors that affect their shapes, such as temperature and pH.

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Figure 10 illustrates how the component of the electric field parallel to the long molecules is absorbed. An electromagnetic wave is composed of oscillating electric and magnetic fields. The electric field is strong compared with the magnetic field and is more effective in exerting force on charges in the molecules. The most affected charged particles are the electrons in the molecules, since electron masses are small. If the electron is forced to oscillate, it can absorb energy from the EM wave. This reduces the fields in the wave and, hence, reduces its intensity. In long molecules, electrons can more easily oscillate parallel to the molecule than in the perpendicular direction. The electrons are bound to the molecule and are more restricted in their movement perpendicular to the molecule. Thus, the electrons can absorb EM waves that have a component of their electric field parallel to the molecule. The electrons are much less responsive to electric fields perpendicular to the molecule and will allow those fields to pass. Thus the axis of the polarizing filter is perpendicular to the length of the molecule.

All we need to solve these problems are the indices of refraction. Air has n1 = 1.00, water has n2 = 1.333, and crown glass has n′2=1.520. The equation [latex]\tan\theta_{\text{b}}=\frac{n_2}{n_1}\\[/latex] can be directly applied to find θb in each case.

17. (a) 2.07 × 10−2 °C/s; (b) Yes, the polarizing filters get hot because they absorb some of the lost energy from the sunlight.

Another interesting phenomenon associated with polarized light is the ability of some crystals to split an unpolarized beam of light into two. Such crystals are said to be birefringent (see Figure 15). Each of the separated rays has a specific polarization. One behaves normally and is called the ordinary ray, whereas the other does not obey Snell’s law and is called the extraordinary ray. Birefringent crystals can be used to produce polarized beams from unpolarized light. Some birefringent materials preferentially absorb one of the polarizations. These materials are called dichroic and can produce polarization by this preferential absorption. This is fundamentally how polarizing filters and other polarizers work. The interested reader is invited to further pursue the numerous properties of materials related to polarization.

There is a range of optical effects used in sunglasses. Besides being Polaroid, other sunglasses have colored pigments embedded in them, while others use non-reflective or even reflective coatings. A recent development is photochromic lenses, which darken in the sunlight and become clear indoors. Photochromic lenses are embedded with organic microcrystalline molecules that change their properties when exposed to UV in sunlight, but become clear in artificial lighting with no UV.

Light-emitting diode (LED) lamps are becoming consistently more available and for all types of light fittings, rather than those specifically designed for them. They are extremely low power (2 W) so represent an exceptionally efficient lighting system (more so even than fluorescent lamps). The lifetime of these lamps can be up to several years, which is important for a user with visual impairment, due to the practical difficulty for them of changing a failed unit (and the potential safety issue of reaching a wall or ceiling luminaire). LED sources are often in a sealed light fitting, so when the lamp fails, the whole fitting needs to be replaced rather than just changing the LED. These lamps do not get very hot so there is less danger of the patient burning their hands, or there being a fire hazard. The LED lamps can be made to emit various ‘white lights’ and is now common to also see these used in illuminated hand-held and stand magnifiers. It is possible to have white LED light created by using combinations of red, green and blue LEDs. LEDs offer white light with a variety of colour temperatures by mixing the amount of red, green and blue LEDs that are being used to create each of these different light sources. Schweizer magnifiers, for example, are available with three alternative colour temperatures: 2700 K which is the incandescent equivalent, 4500 K is the fluorescent equivalent and 6000 K which is a bluish light (i.e. overcast sky in the northern hemisphere).

Figure 6. The effect of rotating two polarizing filters, where the first polarizes the light. (a) All of the polarized light is passed by the second polarizing filter, because its axis is parallel to the first. (b) As the second is rotated, only part of the light is passed. (c) When the second is perpendicular to the first, no light is passed. (d) In this photograph, a polarizing filter is placed above two others. Its axis is perpendicular to the filter on the right (dark area) and parallel to the filter on the left (lighter area). (credit: P.P. Urone)

Figure 7. A polarizing filter transmits only the component of the wave parallel to its axis, , reducing the intensity of any light not polarized parallel to its axis.

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Figure 4. The slender arrow represents a ray of unpolarized light. The bold arrows represent the direction of polarization of the individual waves composing the ray. Since the light is unpolarized, the arrows point in all directions.

Even table-top LED lamps can be battery operated or connected to a USB socket which means the patient can move them to wherever they are required (or even take them on holiday). LEDs are also available on adhesive strips, which are a cheaper alternative to having lighting installed under kitchen wall cupboards to illuminate the worktop, or inside wardrobes to help in selecting clothes. A miniature LED lamp is also available which can be attached to the side of a spectacle frame to illuminate the reading task ( Fig. 7.28 ).

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In flat screen LCD televisions, there is a large light at the back of the TV. The light travels to the front screen through millions of tiny units called pixels (picture elements). One of these is shown in Figure 12 (a) and (b). Each unit has three cells, with red, blue, or green filters, each controlled independently. When the voltage across a liquid crystal is switched off, the liquid crystal passes the light through the particular filter. One can vary the picture contrast by varying the strength of the voltage applied to the liquid crystal.

The effect of slowed adaptation in older eyes is also dramatic: an object has to be 10× brighter to be seen by an 85-year-old compared to a 20-year-old after an equivalent period of dark adaptation ( ). Light adaptation (going from the dimmer indoor environment to bright outdoor space) is also slowed. So uniformity of illumination, and gradual transitions in illuminance level, are very important to individuals with visual impairment.

Terminology The amount of light emitted by a light source is called the luminous flx and is measured in lumens . The efficacy of a particular light source is the quantity of luminous flx which is created by a given input of electrical energy, and this is expressed in lumens per watt . This light now spreads out from the source, and the quantity of light hitting the working surface or task is described as the illuminance, which is defined as the amount of light per unit area. It is measured in lumens per square metre, which are also called lux (lx) . Consider a light source emitting a particular amount of light—luminous flx, measured in lumens—and illuminating the working area from a distance d . If the light source is moved further away from the surface, then the area it illuminates (the area over which the amount of light is spread) will increase. As the distance doubles, the area illuminated increases fourfold, and thus the illuminance decreases by a factor of 4. This represents the inverse square law: illuminance of an object is inversely proportional to the square of the distance of the light source from that object. Illuminance of the surface decreases if it is tilted, because this also increases the area to be illuminated ( Fig. 11.1 ). If the surface is tilted by an angle α (or the light source is placed at an angle α with respect to a perpendicular to the surface) the illuminance will be proportional to the cosine of angle α : this is the cosine law. Fig. 11.1 The illumination by a light source onto a working surface. As the distance of the working surface from the light doubles from d to 2 d , the area illuminated increases by a factor of four. The area illuminated also increases (and so illuminance decreases) when it is tilted by an angle α . Combining these two relationships, it is clear that

Figure 15. Birefringent materials, such as the common mineral calcite, split unpolarized beams of light into two. The ordinary ray behaves as expected, but the extraordinary ray does not obey Snell’s law.

Brewster’s angle: [latex]{\theta }_{\text{b}}={\tan}^{-1}\left(\frac{{n}_{2}}{{n}_{1}}\right)\\[/latex], where n2 is the index of refraction of the medium from which the light is reflected and n1 is the index of refraction of the medium in which the reflected light travels

Polaroid sunglasses are familiar to most of us. They have a special ability to cut the glare of light reflected from water or glass (see Figure 1). Polaroids have this ability because of a wave characteristic of light called polarization. What is polarization? How is it produced? What are some of its uses? The answers to these questions are related to the wave character of light.

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Experimental data obtained by several researchers in a variety of ‘performance versus illuminance’ studies allowed a determination of the level of lighting required to optimally detect a target of a particular size and contrast. When these studies are applied to subjects with ‘normal’ vision, the absolute level of illuminance which will allow a task of ‘normal’ size and contrast to be performed efficiently and safely can be determined, and these results have influenced the lighting codes developed in various countries. These standards usually relate to the working environment, with regulations for domestic lighting being based on energy efficiency. The Illuminating Engineering Society Aged and Partially Sighted Committee have, however, published detailed recommendations on lighting design for these populations, and selected illuminance values are shown in Table 11.1 . Separate values are given for the overall ambient space (A) and the specific task (T). It should be emphasized that these are minimum levels, and may need to be increased in specific cases, especially if visual impairment is more severe.

Light is one type of electromagnetic (EM) wave. As noted earlier, EM waves are transverse waves consisting of varying electric and magnetic fields that oscillate perpendicular to the direction of propagation (see Figure 2). There are specific directions for the oscillations of the electric and magnetic fields. Polarization is the attribute that a wave’s oscillations have a definite direction relative to the direction of propagation of the wave. (This is not the same type of polarization as that discussed for the separation of charges.) Waves having such a direction are said to be polarized. For an EM wave, we define the direction of polarization to be the direction parallel to the electric field. Thus we can think of the electric field arrows as showing the direction of polarization, as in Figure 2.

Figure 1. These two photographs of a river show the effect of a polarizing filter in reducing glare in light reflected from the surface of water. Part (b) of this Figure was taken with a polarizing filter and part (a) was not. As a result, the reflection of clouds and sky observed in part (a) is not observed in part (b). Polarizing sunglasses are particularly useful on snow and water. (credit: Amithshs, Wikimedia Commons)

Figure 14. Optical stress analysis of a plastic lens placed between crossed polarizers. (credit: Infopro, Wikimedia Commons)

Find Polaroid sunglasses and rotate one while holding the other still and look at different surfaces and objects. Explain your observations. What is the difference in angle from when you see a maximum intensity to when you see a minimum intensity? Find a reflective glass surface and do the same. At what angle does the glass need to be oriented to give minimum glare?

Based on the investigations by , Fig. 11.2 shows schematically how an observer’s ability to perform a visual task increases with improvements in the task illuminance: this effect is more dramatic for old compared to young subjects. This general pattern of response can be found with a wide variety of tasks (ranging from laboratory-based studies of searching for a Landolt C of particular orientation among an array of letters of other orientations, to a ‘real-life’ task of scanning components on a conveyor belt looking for those which are incorrectly manufactured), and with a variety of measures of performance (such as the numbers of errors made, or the time taken to perform a search). If the visual task is very easy—using large objects of high contrast—there will be very little difference between the performance of the different age groups, and the response will appear as in point (c) in Fig. 11.2 even at relatively low luminance. If the detail within the task is small, and contrast is low, the characteristic response is that at point (a) of Fig. 11.2 , and the illuminance must be increased to produce an improvement.

Figure 12. (a) Polarized light is rotated 90º by a liquid crystal and then passed by a polarizing filter that has its axis perpendicular to the original polarization direction. (b) When a voltage is applied to the liquid crystal, the polarized light is not rotated and is blocked by the filter, making the region dark in comparison with its surroundings. (c) LCDs can be made color specific, small, and fast enough to use in laptop computers and TVs. (credit: Jon Sullivan)

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polarization: the attribute that wave oscillations have a definite direction relative to the direction of propagation of the wave