Thursday, 18 June 2009

Physics – total internal reflection and colours

Total internal reflection By Shell’s Law, we know that the value of sin x can’t be larger than 1. But if one side of the equation is larger than the refractive index on another side, we’ll found that another side of the equation can never equal to another side, and the total internal reflection occur. It’s a “reflection” so that it obeys the law of reflection. For example, the light strike from glass (R.I. 1.7) to air, 1.7sin (angle of incidence) =1sin (angle of refraction), if the angle of incidence is big enough, equation can’t hold. The “big enough” limit is called the critical angle, and c=sin-1 (1/x). It follows that when the R.I. is bigger, critical angle is smaller and total internal reflection is easier to happen. This explained why it mostly happen in medium with higher R.I.. Applications: 1) Views under water – when you’re under water, you may not see the image above water if the angle of incidence is big enough, and the range that you can see image above water is in cone shape, with the axis from your eyes, perpendicular to the water surface. (This is because the angle of incidence is limited.) 2) Periscope – If we use glass with enough big R.I.(bigger than 1.5, usually, is enough), we can make two 45-90-45 triangular prisms to reflect light just like plane mirrors. 3) Diamond – it’s so bright because it’s R.I. is too high (above 2) such that all light (especially after process) will be reflected back. 4) “Cat’s eye” in front of the car uses the same rule to give out strong light. Optical fibres Optical fibre is a tube-like device which can transmit light. It's made by glass and some other material, layer by layer. Since total internal reflection always occur inside the tube, and the tube can be bent into a certain angle, it can transmit light in the curved path. There is various application of optical fibre. The most important use is the usage on telecommunication services. Comparing with the traditional wire, it's much cheaper since the traditional wire uses a lot of copper. Even the material cost is more expensive than the production cost of optical fibre considering the same volume. Another important use is endoscope for surgery. Colours When a narrow white light passes through a triangular (△ shape) glass prism, it will changed into a fan of colours, from the top to bottom; red, orange, yellow, green, blue, indigo and purple. This band of colours is called the colour spectrum, and we say that it is the dispersion of the white light. One of its applications is the rainbow. After raining, the air is full of small water droplets. They refracted (twice; in and out the water droplets), reflected (total internal reflection within the water droplets) and disperse the sun light to colour spectrum into our eyes. White light is the mixture of three primary coloured lights, red, blue and green. They can produce all colours. Red and blue produces magenta, red and green produces yellow, blue and green produces cyan, and all three together produce white light. Colour televisions produces different colours on the TVs by giving signals to three phosphor dots inside the TV and give out red, blue and green colours. We sense colours also because the three types of cones cells and receive the three kind of primary coloured lights. Those who do not have enough cones cells is called to have colour blindness, and it’s inherited and can’t be corrected. Those who have defect on all three types of cones cells are called total colour blindness. We see object because they reflect that light to us. For example, apples reflects red light to us. Other lights will be absorbed (and turned into heat energy). Another example is that white object reflects everything to us and thus we see it’s white, which is the mixture of red, blue and green light. “The object with colour N, shined by colour X, will reflect light that N and X contains commonly and absorb the remaining part.” E.g. When a cyan object shined by yellow light, it will reflect green light (which cyan and yellow contains commonly) and absorb red light (the remaining part of yellow.) Colour filters are used to let certain lights to pass through and absorb the remaining light. “The colour filters with colour N, shined by colour X, will let light that N and X contains commonly to pass through, and absorb the remaining part.” The function between a normal object and a colour filter a nearly the same, but colour filters is designed to let light to pass through it.

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