1. Reflection from Curved Surfaces and Fibre Optics Preliminary Physics

2. Spherical Mirrors The two types of spherical mirrors are shown in the diagram on the right. Spherical mirrors can be thought of as a portion of a sphere which was sliced away and then silvered on one of the sides to form a reflecting surface. Concave mirrors were silvered on the inside of the sphere and convex mirrors were silvered on the outside of the sphere.

3. Beginning a study of spherical mirrors demands that you first become acquainted with some terminology which will be periodically used. Principal axisCentre of CurvatureVertex Focal PointRadius of CurvatureFocal Length

4. If a concave mirror is thought of as being a slice of a sphere, then there would be a line passing through the centre of the sphere and attaching to the mirror in the exact centre of the mirror. This line is known as the principal axis. The point in the centre of sphere from which the mirror was sliced is known as the centre of curvature and is denoted by the letter C in the diagram.

5. The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is denoted by the letter A in the diagram below. The vertex is the geometric centre of the mirror. Midway between the vertex and the centre of curvature is a point known as the focal point; the focal point is denoted by the letter F in the diagram

6. The distance from the vertex to the center of curvature is known as the radius of curvature (abbreviated by "R"). The radius of curvature is the radius of the sphere from which the mirror was cut.

7. Finally, the distance from the mirror to the focal point is known as the focal length (abbreviated by "f"). Since the focal point is the midpoint of the line segment adjoining the vertex and the centre of curvature, the focal length would be one-half the radius of curvature.

8. The focal point is the point in space at which light incident towards the mirror and travelling parallel to the principal axis will meet after reflection. The diagram at the right depicts this principle. In fact, if some light from the Sun was collected by a concave mirror, then it would converge at the focal point. Because the Sun is such a large distance from the Earth, any light rays from the Sun which strike the mirror will essentially be travelling parallel to the principal axis. As such, this light should reflect through the focal point.

9. The simpler method relies on two simple rules of reflection for concave mirrors. They are: Any incident ray travelling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection. Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.

10. Total Internal Reflection Total internal reflection (TIR) is the phenomenon which involves the reflection of all the incident light off the boundary. TIR only takes place when both of the following two conditions are met:  a light ray is in the more dense medium and approaching the less dense medium.  the angle of incidence for the light ray is greater than the so-called critical angle.

11. TIR In our introduction to TIR, we used the example of light travelling through water towards the boundary with a less dense material such as air. When the angle of incidence in water reaches a certain critical value, the refracted ray lies along the boundary, having an angle of refraction of 90- degrees. This angle of incidence is known as the critical angle; it is the largest angle of incidence for which refraction can still occur. For any angle of incidence greater than the critical angle, light will undergo total internal reflection.

13. Critical Angle So the critical angle is defined as the angle of incidence which provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6- degrees. For the crown glass-water boundary, the critical angle is 61.0-degrees. The actual value of the critical angle is dependent upon the combination of materials present on each side of the boundary.

14. To understand total internal reflection, we will begin with a thought experiment. Suppose that a laser beam is submerged in a tank of water (don't do this at home) and pointed upwards towards water-air boundary. Then suppose that the angle at which the beam is directed upwards is slowly altered, beginning with small angles of incidence and proceeding towards larger and larger angles of incidence.

15. Fibre Optics You hear about fibre-optic cables whenever people talk about the telephone system, the cable TV system or the Internet. Fibre-optic lines are strands of optically pure glass as thin as a human hair that carry digital information over long distances. They are also used in medical imaging and mechanical engineering inspection.

16. What are Fibre Optics? Fibre optics (optical fibres) are long, thin strands of very pure glass about the diameter of a human hair. They are arranged in bundles called optical cables and used to transmit light signals over long distances.

17. Optic Fibre Parts It has the following parts: Core - Thin glass centre of the fibre where the light travels Cladding - Outer optical material surrounding the core that reflects the light back into the core Buffer coating - Plastic coating that protects the fibre from damage and moisture Hundreds or thousands of these optical fibres are arranged in bundles in optical cables. The bundles are protected by the cable's outer covering, called a jacket. Optical fibres come in two types:  Single-mode fibres  Multi-mode fibres

18. Types of Optic Fibres Single-mode fibres have small cores (about 3.5 x 10 -4 inches or 9 microns in diameter) and transmit infrared laser light (wavelength = 1,300 to 1,550 nanometres). Multi-mode fibres have larger cores (about 2.5 x 10 -3 inches or 62.5 microns in diameter) and transmit infrared light (wavelength = 850 to 1,300 nm) from light-emitting diodes (LEDs). Some optical fibres can be made from plastic. These fibres have a large core (0.04 inches or 1 mm diameter) and transmit visible red light (wavelength = 650 nm) from LEDs. Let's look at how an optical fibre works.

19. Total Internal Reflection The light in a fibre-optic cable travels through the core by constantly bouncing from the cladding, a principle called total internal reflection. Because the cladding does not absorb any light from the core, the light wave can travel great distances.

20. Problems? However, some of the light signal degrades within the fibre, mostly due to impurities in the glass. The extent that the signal degrades depends on the purity of the glass and the wavelength of the transmitted light (for example, 850 nm = 60 to 75 percent/km; 1,300 nm = 50 to 60 percent/km; 1,550 nm is greater than 50 percent/km). Some premium optical fibres show much less signal degradation -- less than 10 percent/km at 1,550 nm.

21. Advantages of Fibre Optics Why are fibre-optic systems revolutionizing telecommunications? Compared to conventional metal wire (copper wire), optical fibres are:  Less expensive - Several miles of optical cable can be made cheaper than equivalent lengths of copper wire. This saves your provider (cable TV, Internet) and you money.  Thinner - Optical fibres can be drawn to smaller diameters than copper wire.  Higher carrying capacity - Because optical fibres are thinner than copper wires, more fibres can be bundled into a given-diameter cable than copper wires. This allows more phone lines to go over the same cable or more channels to come through the cable into your cable TV box.

22. Advantages of Fibre Optics Less signal degradation - The loss of signal in optical fibre is less than in copper wire. Light signals - Unlike electrical signals in copper wires, light signals from one fibre do not interfere with those of other fibres in the same cable. This means clearer phone conversations or TV reception. Low power - Because signals in optical fibres degrade less, lower-power transmitters can be used instead of the high-voltage electrical transmitters needed for copper wires. Again, this saves your provider and you money.

23. Advantages of Fibre Optics Digital signals - Optical fibres are ideally suited for carrying digital information, which is especially useful in computer networks. Non-flammable - Because no electricity is passed through optical fibres, there is no fire hazard. Lightweight - An optical cable weighs less than a comparable copper wire cable. Fibre-optic cables take up less space in the ground. Flexible - Because fibre optics are so flexible and can transmit and receive light, they are used in many flexible digital cameras for the following purposes:digital cameras Medical imaging - in bronchoscopes, endoscopes, laparoscopes Mechanical imaging - inspecting mechanical welds in pipes and engines (in airplanes, rockets, space shuttles, cars)airplanesrocketsspace shuttles cars Plumbing - to inspect sewer linessewer lines

24. Advantages of Fibre Optics Because of these advantages, you see fibre optics in many industries, most notably telecommunications and computer networks. For example, if you telephone Europe from Australia (or vice versa) and the signal is bounced off a communications satellite, you often hear an echo on the line. But with fibre-optic cables, you would have a direct connection with no echoes.