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Example Physics Essay

The aim of this investigation is to show the variation of light intensity with distance; namely the inverse square law of light intensity with distance.

Background Theory

Light emitted from any kind ofsource, e.g. the sun, a light bulb, is a form of energy. Everyday problems suchas lighting required for various forms of labouring or street illumination,require one to able to determine and evaluate the intensity of light emitted byany light source or even the illumination of a given surface. A special groupof studies is formed around these issues and it is called photometry.

Luminous flux is a scalarquantity which measures the time rate of light flow from the source. As allmeasures of energy transferred over a period of time, luminous flux is measuredin Joules/Seconds or Watts (SI units). It can therefore safely be said thatluminous flux is a measure of light power.

Visible light consists of severaldifferent colours, each representing a different wavelength of the radiationspectrum. For example red colour has a wavelength 610-700 nm, similarly yellow550-590 nm and blue 450-500 nm. The human eye demonstrates different levels ofsensitivity to the various colours of the spectra. More specifically, themaximum sensitivity is observed in the yellow-green colour (i.e. 555nm). Fromall the above, it is clear that there is the need to define a unit associatingand standardising the visual sensitivity of the various wavelengths to thelight power which are measured in Watt's; this unit is called the specialluminous flux unit of the lumen (lm). One lumen is equivalent to1/680 Watt of light with a wavelength of 555 nm. This special relationshipbetween illumination and visual response renders the lumen the preferredphotometric unit of luminous flux for practical applications. On top of thatone of the most widely used light sources in everyday life such as the electriclight bulb emits light which consists of many different wavelengths.

A measure of the luminousstrength of any light source is called the light sources intensity. At thispoint, it should be said that the intensity of a light source depends on thequantity of lumens emitted within a finite angular region which is formed by asolid angle. To give a visual representation of the solid angle, recall that ina bi-dimensional plane the plane angle qis used for all kinds of angular measurements. A further useful reminderregards the arc length s; namely for a circle of radius r the arclength s is calculating by the formula

S = r * q -Equation. 1

(qis measured in radians)

Now, in a three dimensional planethe solid angle W is similarly used forangular measurements. Corresponding to the q planeangle, each section of surface area A of a sphere of radius r iscalculating by using the following formula;

A= r²*W -Equation. 2

(remember that W is measured in steradians)

By definition one steradian isthe solid angle subtended by an area of the spherical surface equal to thesquare of the radius of the sphere.

Taking into account all theabovementioned, the luminous intensity I of a light source (small enough to beconsidered as a point source) pointing towards the solid angle is given by:

I = F/ W -Equation. 3

Where F is the flux measured inlumens. It is clear that the luminous intensity unit is lumen /steradian. Thisunit used to be called a candle, as it was defined in the context of lightemitted from carbon filament lamps.

Generally speaking, luminousintensity in any particular direction is called the candle power of the source.The corresponding unit in the SI system is called the candela (cd)which is the luminous intensity emitted by 1/60 cm² of platinum at atemperature of 2054K (which is the fusion point of platinum).

A uniform light source (smallenough to be considered as a point source) whose luminous intensity is equal toone candela, is able to produce a luminous flux of one lumen through each solidangle. The equation shown below is the mathematical expression of the abovedefinition:

F = W * I -Equation. 4

Where I is equal to one cd and W is equal to one sr.

In similar terms the total flux F_tof a uniform light source with an intensity I can be calculated with the aid ofthe following formula.

F_t = W_t* I - Equation. 5

And taking into account that thetotal solid angle W_t of asphere is 4p sr, the above formulabecomes

F_t = 4p * I -Equation. 6

When a surface is irradiated withvisible light it is said to be illuminated. For any given surface, theilluminance E (which is also called illumination) is intuitively understood anddefined to be the flux indenting on the surface divided by the total area ofthe surface.

E = F / A - Equation. 7

In the case where the severallight sources are present and illuminate the same surface, the totalilluminance is calculated by adding up all of the individual sourceilluminations. The SI unit allocated the illuminance is the lux (lx)where one lx is equal to 1 lm / 1 m².

Another way of expressingillumination in the context of light sources intensity and the distance fromthe light source can be derived by forming a combination of the last fewmentioned equations:

E = F / A = I * W / A = I / r²-Equation. 8

Where r is the distance measuredfrom the source or the radius of a sphere whose total area is A (W = A / r²). An important sidenoteat this point is that 1fc equals 1cd/ft² and also 1lx is equal to1cd/ m².

It is evident that theillumination is inversely proportional to the square of the measured distancefrom the light source. In the case of constant light source intensity I, it canbe said that:

E₂/E₁ = r₁²/r₂²= (r₁/r₂)² - Equation. 9

In the real world, the incidentlight is very rarely normal to a surface; nearly always light impacts on asurface at an angle of incidence q.

In this case the illuminance iscalculated by:

E = I* cos q/ r²-Equation. 10

To sum up, there are several wayswhich can be employed in order to measure illumination. Nearly all of them arebased on the photoelectric effect originally discovered by Albert Einstein (forwhich he was awarded a Nobel Prize in 1921). In a few words when light strikesa material electron emission is observed and electric current flows if there isa circuit present. This current is proportional to the incident light flux andto the work functionof the material; the intensity of the resulted current flow is measured byinstruments calibrated in illumination units.

Apparatus Components:

Light Sensor - Light Dependent Resistance (LDR)

Light bulb

Ruler

Power supply

Voltmeter

Ammeter

Connecting wires and Inline conductors

Two Vertical Stands

Black Paper

Experimental Apparatus

The experimental apparatusconsisted off various parts. The basis of the light reception circuit was a LightDependent Resistor (LDR) which is the essential part of the apparatus since inenables the measurement of the light's intensity.

To give a brief introduction tothis type of devices, it should be said that all kinds of materials exhibitsome kind of resistance to electric current flow (which by definition isorientated flow of electrons). The particularity of an LDR device lays in the fact that its resistance is notconstant; instead, it varies its value according to the light's intensity thatimpacts on it. Generally speaking, LDR devices can be categorized in two maindivisions: negative and positive coefficient. The former decrease theirresistance as the light's intensity grows bigger; on the other hand, the latterincrease their resistance as the light's intensity becomes greater. At themicroscopic level, such a device consists of semi-conducting material likedoped-silicon (the most commonly used material for electronic applications).When light impacts on the device material, this energy is absorbed by thecovalent bonded electrons. Subsequently, this excessive energy breaks the bondsbetween the electrons and creates free electrons inside the material. Theseelectrons are free to move inside the material and hence increase theresistivity of the material since they are no longer bonded.

Another essential part of the apparatus is the lightsource, which in this particular cause was an incandescent lamp (these lampsare the most commonly used ones found in most everyday applications). The basiccomponent of an incandescent lamp is the wire filament which is usually made oftungsten; this filament is sealed in glass bulb. Now, the bulb itself is filledwith a mixture of low pressure argon and nitrogen in gaseous form. The use ofthose two gases is to delay the evaporation of the metal filament as well as itoxidation. Ones current begins to flow through the tungsten filament, it getsso hot that it looks white. Under these operating conditions the filamentitself ranges in temperature from 2500-3000 degrees Celsius. All incandescentlamps have continuous spectrum which lies primarily in the infrared region ofthe electromagnetic spectrum. The basic drawback of these devices is they poorefficiency, since more than 95% of the lamps energy is lost to the ambientenvironment in the form of heat.

The detailed apparatus used for this investigation is shownschematically in figure.1. According to this figure the light source(incandescent lamp (light bulbselectrical characteristics required here) ) is placed on a fixed stand and is kept at a verticalupright position looking upwards. It is evident that ones the bulb is switch onthe light will be emitted isotropically towards all directions. A power supply(( power supply's electricalcharacteristics required here) ) was used for poweringup the light bulb and providing variable voltage values. In that way, as willbe explained later, the intensity of the light emitted by the bulb will notstay constant and neither will the voltage across the LDR.

Opposite thelight bulb, on another stand the LDR device has kept fixed in place with theaid of cohesive material (blu tack). The LDR device was placed normally to thelight bulb so that the angle of incidence of the light coming of the sourceremains constant and normal throughout the experimental measurements.

Anotherobservation that can be made from Figure.1 is the interconnection between theLDR device, the voltmeter, the ammeter and the power supply. More specifically,in order for the LDR to function properly, a voltage was applied across thereceiver circuit ( 4 Volts power pack in our case). The voltmeter was connectedacross the LDR device in order to constantly measure the value of the voltageacross the LDR. These variations were due to the alternations to the intensityof the incident light (since the resistance value was changing). The voltmeterideally would have infinite resistance, however in reality its resistance isfinite and thus small deviations of the indicated voltage from the real valuewere expected.

Another quantityunder monitoring was the current flowing into the LDR device. For this purposean ammeter was placed in series with the LDR. Its rule was very important sincethe current flow into the LDR device had to remain constant throughout theexperimental measurements. Again, the ideal ammeter would not have anyimpendence at all. In reality all ammeter demonstrate a finite albeit verysmall value of resistance: thus deviation of the indicated value from theactual one should be expected.

(Missing resistance for potential divider?)

A veryinteresting configuration (and very widely used) for light intensitymeasurements using the same components as the ones available for this practicalcan be seen in Figure.1 with a little insight. A closer look to the receivercircuit reveals that a potential divider is formed by the way that the abovementioned components are connected. On a sidenote, measuring the current comingout of the LDR device would be feasible and relatively easy since the outputcurrent would be directly proportional to the value of the LDR resistance. Abetter way would be to measure the output voltage which happens to be thevoltage across the LDR (i.e. the value monitor by the voltmeter). In this casethe voltage is proportional to the current flowing through the LDR device. Thesecond resistance required to form the potential divider comes from the finiteinternal resistance of the ammeter. The value of the output voltage V_outcan be calculated by using the standard potential divider formula shown below:

V_out = R_LDR / (R_LDR + R_AMMETER)* V_in- Equation. 11

Where V_inis the voltage applied across the receiver circuit, R_LDRand R_AMMETERare the resistance of the LDR device and the internal resistance of the ammeterrespectively.

Since the aim ofthose measurements is to investigate the relationship between the light intensitywith distance, despite the fact that both the light bulb and LDR are kept fixedvertically the stand of the light bulb was able to be translated horizontally.For the purpose of the experiments the translation of the light bulb was madeparallel with a ruler which was placed between the two stands. Thisconfiguration was quite optimal since it allowed the exact distance betweenlight source and receiver to be know throughout the experiments.

In all opticalexperiments one of most fundamental error is the background illumination andthe interference of other light sources. For this reason the apparatus wassurrounded by black paper.

Experimental Procedure

The LDR sensorand the light bulb have to be at the same vertical height during all experimentalmeasurements. One key point to notice is in that way the light bulb behaves asmore like a point source of light, justifying the use of all mathematicalequations. The LDR sensor has to point towards the light bulb at all times.

Having set upthe experimental apparatus and chosen the range of the distance between thelight bulb and the LDR sensor, a reference measurement of the LDR sensor wasmade having the light bulb switched off. Depending on the power of the lightbulb a starting distance of 10 cm was deemed to be sufficient for thecalibration purposes. Progressively, after performing the calibration thisdistance as explained below increased. Similarly, the rest of the experimentalapparatus's components (i.e. receiver device, voltmeter, ammeter, etc.) werealso switched off during this very crucial calibration phase of the practical;generally speaking it is very good and common practice as well as much morepreferable to carry out the calibration and experimental procedure inconditions of total darkness. The previous step insured that the backgroundillumination was measured and this value would have to be deducted from allfurther measurements. Hence the error of the measurements is eliminated andtheir credibility is increased by a great degree.

The light bulbwas initially switched on by applying a specific voltage across it;subsequently the exact distance between the light bulb and the LDR was measuredusing the ruler. The next and most important step at this stage was to measurethe value of the potential difference across the LDR device for this specificposition of the light bulb. For reasons of reference, the value of the ammeterwas also recorded.

The position ofthe light bulb stand was then altered along the ruler in constant and knowsintervals of distance. For each known distance the above measurements had to berepeated over and over. At this stage it would be useful to emphasize that theacquisition of the above data can be made for more than one time per knowndistance r, since averaging of data decreases the error percentage in theexperimental measurements obtained. In that way, a comprehensive chart or tablecan be formed associating distance values (between the two stands) to outputvoltage values.