An Investigation into the Effect on the Critical Angle by Changing the Colour of Light

An Investigation into the Effect on the Critical Angle by Changing the Colour of Light
An Investigation into the Effect on the Critical Angle by Changing the Colour of Light Aim: To investigate the factors affecting the size of the critical angle through a median of Perspex Background Information: The critical angle of light is when it hits a different median from the one it had been travelling in, for example glass to air at a certain angle that causes total internal reflection. This angle is different for all lights and medians. Total internal reflection is when a beam of light travelling through a certain median is reflected back at an angle that is equal to its incidence instead of just being refracted and then passing out the other side. This phenomenon is used to transmit information through fibre optic cables.
Fibre Optic cables have a beam of light sent down them in which the information is encoded. The beam of light is angled to hit the side of the cable at an angle greater than medians critical angle (42Ëš). The beam then reflects off one side of the cable then to the opposite side. Again the angle of incidence is greater than the critical angle. This is then repeated all the way to the end of the cable where the information is needed. Practical applications include digital audio transmitters which allow CD quality sound to be sent from one place to the other, with hardly any loss of quality. Other applications include Cats Eyes which are reflective road markings. These employ total internal reflection to give drives a better idea of where the road markings are, when driving in the dark. The Cats Eye works by reflecting the light from the cars head lamps through 180Ëš and back to the eyes of the driver to alert him or her when the centre of the road is. [image] This diagram shows how the light rays entering a fibre optic cable are reflected using total internal reflection over and over again Source: [image] Source : This diagram shows the light beam loosing its refracted ray and gaining the ray that shows total internal reflection. This is happening as the angle of incidence gets bigger. The refracted ray in shown in red and the ray that shows total internal reflection is green. The factors that affect the angle when total internal refraction is reached (the critical angle) are:
Median- the type of median that the light is travelling through
affects the angle because of differences in the composition of the
material. A median with a higher density will have a smaller
critical angle than one with less density because the more dense
the median the more it refracts light.
The shape- the shape of the median effects where the light enters
the median and this location could affect the critical angle. It
also determines how far the light beam has to travel before
striking the other side of the median, this also could have some
bearing on the critical angle.
The colour of the light:- different colours of light have
different wave lengths, this correlates to their position in the
electromagnetic spectrum with red light having the longest
wavelength and violet light having the shortest wavelength. This
factor makes a difference to the critical angle because the higher
the wavelength the less easy it is to refract the light with the
higher wavelength.
The size of the light beam- this effects the critical angle
because of the way that this could make the light strike the face
of the median.
Intensity of the light- the intensity of light could effect the
critical angle because the more intense the light, the more easily
the light is refracted. This would be marginal.
Distance form the light source- again this would effect the way in
which the light would strike the face of the median. This could
marginally effect the critical angle.
The two variables that could easily be altered in a school laboratory situation would be the shape of the median and the colour of the light entering the median. I have chosen to change the colour of the light because I feel that this would give me a wider set of results. Apparatus: Power Pack- supplies power to the Ray Box (set to 12 volts) Ray Box- generates a beam of light Perspex Semi Circle- this is the median used to create total internal reflection Coloured light filter- used to generate the coloured light of your choice Protractor- used to measure any desired angles Paper- an A4 sheet to mark any angles on from the experiment Apparatus Diagram: Method: Set the apparatus up as shown in the diagram and select the desired colour to test. Insert the filter into the ray box. Engage the ray box; the position of the filter may need to be manipulated to achieve the optimum setting for the experiment. Direct the beam of light to the rounded face of the Perspex semi circle. Move the beam of light to increase the angle until there is no angle of refraction and all the light is reflected back out of the Perspex. This is when the critical angle or the angle of total internal reflection has been reached. This angle must now be recorded. Fair Testing: To keep this experiment a fair test it is important to keep all the variables the same and only change the one that is being tested (colour of the light). Ensure this by keeping the median the same throughout the investigation, always use Perspex. Use a semicircular block for all experimentation. Keep the size of the light beam the same by using the same light source in each experiment carried out. The light intensity can be kept constant by setting the voltage the light supply the same and by using the same ray box to supply it. Safety: Bright light can be dangerous; do not look directly at the bulb when it is on because this could cause irreversible eye damage. Do not exceed the stated voltage of the bulb this could cause the bulb to ?blow? and possibly overload the power pack. Do not short the terminals of the power supply, this is dangerous and causes damage to the power pack. [image]Prediction: I predict that the critical angle for red light will have the smallest critical angle and blue light to have the largest critical angle due to their position in the spectrum, red being on the outside and blue on the inside. The light colours on the outside are bent the most because of their larger wavelengths, the light colours on the inside are bent the least because of their smaller wavelengths. Light is a type of electromagnetic radiation and is in the electromagnetic spectrum between Infra Red Light and Ultra Violet Light (see diagram). This means they travel in waves, waves have a particular wavelength, and the wavelength determines how easily the light rays are bent. Red light is bent quite easily and blue is not bent so easily because of their different wavelengths. To reach the critical angle the light has to bend sufficiently to achieve total internal reflection. If the light is not bent in easily it will take a larger angle of incidence to reach total internal reflection. This diagram shows the wavelengths of the different colours of light, which is the basis of my investigation. (Source: visible spectrum from red (at left) to violet (at right). Colour Wavelength (nm) Red 750 Orange 700 Yellow 650 Green 600 Colour Wavelength (nm) Blue 450 Indigo 425 Violet 400 The tables above show the wavelengths of each and every colour in the visible spectrum Preliminary Results: I collected some preliminary results to narrow the range in which I had to search for the critical angle. This was to save time and give me an idea of the critical angle with white light, the control. Here are my results: Angle Of Incidence (Ëš) Angle Of Refraction (Ëš) Angle Of reflection (Ëš) 30 30 - 35 35 35 40 40 40 45 45 45 50 - 50 These results show that I should look for the critical between the angle of 35Ëš and 45Ëš. (See also results sheet) This is a graph to show a prediction of the critical angle of coloured light: [image] Results: I chose to use red, green and blue light because they are the primary colours of light Light Colour Result One(Ëš) Result Two(Ëš) Result Three(Ëš) Average (Ëš) Red 43.0 43.0 42.0 42.6 Green 43.0 44.0 43.5 43.5 Blue 44.0 39.0 45.0 44.5 The result I have highlighted in yellow is an anomalous result and have decided to exclude it from my final average because it does not fit the pattern of the other results and my preliminary results. I thought it would throw my average out and would not be a true representation of the rest of the results. Conclusion: From the results I have collected I have concluded that the colour of light does effect the critical angle. This also supports my prediction because the light that had the smallest critical angle was the one that had the largest wavelength (red) and the light with the largest critical angle had the smallest wavelength. This occurs because the smaller the wavelength the less easily the light is refracted, therefore the blue light entered the median at a larger critical angle to achieve total internal reflection. The red light had a smaller critical angle because of its longer wavelength. A longer wavelength means that it can refract easier and reach the critical angle sooner. [image]This diagram shows the colours of the spectrum as they disperse when the exit a prism. It shows that red light is bent the most, because of its small wavelength. It has a lower critical angle because it needs less bending to reach the critical angle because of its ability to bend. This is why it first in the spectrum because it disperses easily so it?s the first to leave the prism. This can also be applied to blue light, but in reverse. Blue can be seen bending the least so it needs a larger critical angle to get it to the point when it reaches total internal reflection. I have one result that did not fit the pattern among the results I collected. I tried to keep these types of results to a minimum but it was inevitable that some could slip through. This result was probably caused by human error, for a full breakdown of possible causes see my Evaluation. Evaluation: Not every result I took for each colour of light was the same for the three experiments I performed. This means, that I have some anomalous results. The following section explains possible reasons for these.
The measuring equipment that I had access to could only measure
accurately to the nearest half degree. This could have affected
the accuracy in which I was able to measure the critical angle.
Slight imperfections in the Perspex could affect the way that the
light entered the median by slightly changing the angle that the
light is bent through. In turn the critical angle could have
become altered, but this would be marginal.
The light beam that was provided by the ray box could be affected
by the bulb in the ray box, how old it is, resistance in the wires
connecting it the power pack etc. Providing a dimmer or brighter
light may have led to angles of refraction disappearing before
they are supposed to because they were too dim to be seen.
The power packs that I have used could have differed slightly,
supplying a brighter or dimmer light ray causing the same problems
as described above.
Using certain colour filters that were different thicknesses could
have affected the angle of entry to the median and the critical
angle because the light would have diffracted slightly differently
when passing through the colour filter. This would be marginal,
If I repeat this experiment I will try to control the above areas of error by: Â? Devising a way to measure more accurately, possibly by using aids such as computers to help me obtain more accurate results for my experiments. Â? Using the newest block of Perspex to minimize the imperfections in it. This is not always practical in a school laboratory. Â? Using the same ray box for every experiment will ensure the imperfections in the ray box will be applied to all the results. Â? Using the same power pack for each experiment will ensure that none of the other experiments will have a different brightness of light ray. Â? Using colour filter with the same thickness and make sure that they are as thin as possible all the way through the experiment to minimise the refraction that could occur while the light is passing in and out of the colour filter. I think the main reason for my errors was how accurately I could measure the angles that were taken during the experiment. This is because with the equipment I had access to, I was unable to measure anything more accurate than half a degree. To extend the experiment and enforce my conclusion I would increase the range of colours I tested to see if the trend is the same all the way through the spectrum. It would also be interesting to try mixes of colours (for example magenta and cyan) to see if there is any correlation between the critical angle of the colours that make up the secondary colour (two primary colours mixed together= a secondary colour).

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