Total Internal Reflection and Fibre Optics, Physics 10 1/ Total Internal Reflection Activity :: Investigation : Total Internal Reflection Work in groups of four. Each group will need a raybox (or torch) with slit, triangular glass prism and protractor. If you do not have a raybox, use a torch and stick two pieces of tape over the lens so that only a thin beam of light is visible. Aim: To investigate total internal reflection. Method: Place the raybox next to the glass block so that the light shines right through without any refraction. See ”Position 1” in diagram. Move the raybox such that the light is refracted by the glass. See ”Position 2”. Move the raybox further and observe what happens. Move the raybox until the refracted ray seems to disappear. See ”Position 4”. The angle of the incident light is called the critical angle. Move the raybox further and observe what happens. See ”Position 5”. The light shines back into the glass block. This is called total internal reflection. When we increase the angle of incidence, we reach a point where the angle of refraction is 90◦ and the refracted ray runs along the surface of the medium. This angle of incidence is called the critical angle. Definition: Critical Angle The critical angle is the angle of incidence where the angle of reflection is 90◦. The light must shine from a dense to a less dense medium If the angle of incidence is bigger than this critical angle, the refracted ray will not emerge from the medium, but will be reflected back into the medium. This is called total internal reflection. Total internal reflection takes place when light shines from an optically denser medium to an optically less dense medium. the angle of incidence is greater than the critical angle. Definition: Total Internal Reflection Total internal reflection takes place when light is reflected back into the medium because the angle of incidence is greater than the critical angle. Figure 7.22: Diagrams to show the critical angle and total internal reflection. Each medium has its own unique critical angle. For example, the critical angle for glass is 42◦, and that of water is 48,8◦. We can calculate the critical angle for any medium. Calculating the Critical Angle Now we shall learn how to derive the value of the critical angle for two given media. The process is fairly simple and involves just the use of Snell’s Law that we have already studied. To recap, Snell’s Law states: n1sin θ1 = n2sin θ2 where n1 is the refractive index of material 1, n2 is the refractive index of material 2, θ1 is the angle of incidence and θ2 is the angle of refraction. For total internal reflection we know that the angle of incidence is the critical angle. So, θ1 = θ$_{c}$. However, we also know that the angle of refraction at the critical angle is 90◦. So we have: θ2 = 90◦. We can then write Snell’s Law as: n1sin θ$_{c}$ = n2 sin 90◦ Solving for θ$_{c }$gives: Important: Take care that for total internal reflection the incident ray is always in the denser medium. Worked Example 1: Critical Angle 1 Question: Given that the refractive indices of air and water are 1 and 1,33, respectively, find the critical angle. Answer Step 1 : Determine how to approach the problem We know that the critical angle is given by: θ$_{c}$ = sin$^{−1}$(n2/n1) Step 2 : Solve the problem θ$_{c}$ = sin$^{−1}$(n2/n1) = 48,8◦ Step 3 : Write the final answer The critical angle for light travelling from water to air is 48,8◦. Worked Example 2: Critical Angle 2 Question: Complete the following ray diagrams to show the path of light in each situation. Answer Step 1 : Identify what is given and what is asked The critical angle for water is 48,8◦. We are asked to complete the diagrams. For incident angles smaller than 48,8◦ refraction will occur. For incident angles greater than 48,8◦ total internal reflection will occur. For incident angles equal to 48,8◦ refraction will occur at 90◦. The light must travel from a high optical density to a lower one. Step 2 : Complete the diagrams Refraction occurs (ray is bent away from the normal) Total internal reflection occurs Refraction towards the normal (air is less dense than water) 2/ Fibre Optics Total internal reflection is a powerful tool since it can be used to confine light. One of the most common applications of total internal reflection is in fibre optics. An optical fibre is a thin, transparent fibre, usually made of glass or plastic, for transmitting light. Optical fibres are usually thinner than a human hair! The construction of a single optical fibre is shown in Figure 7.23. The basic functional structure of an optical fibre consists of an outer protective cladding and an inner core through which light pulses travel. The overall diameter of the fibre is about 125 µm (125 × 10$^{−6}$m) and that of the core is just about 10 µm (10 × 10$^{−6}$m). The mode of operation of the optical fibres, as mentioned above, depends on the phenomenon of total internal reflection. The difference in refractive index of the cladding and the core allows total internal reflection in the same way as happens at an air-water surface. If light is incident on a cable end with an angle of incidence greater than the critical angle then the light will remain trapped inside the glass strand. In this way, light travels very quickly down the length of the cable. 3/ Fibre Optics in Telecommunications Optical fibres are most common in telecommunications, because information can be transported over long distances, with minimal loss of data. The minimised loss of data gives optical fibres an advantage over conventional cables. Data is transmitted from one end of the fibre to another in the form of laser pulses. A single strand is capable of handling over 3000 simultaneous transmissions which is a huge improvement over the conventional co-axial cables. Multiple signal transmission is achieved by sending individual light pulses at slightly different angles. For example if one of the pulses makes a 72,23◦ angle of incidence then a separate pulse can be sent at an angle of 72,26 ◦! The transmitted data is received almost instantaneously at the other end of the cable since the information coded onto the laser travels at the speed of light! During transmission over long distances repeater stations are used to amplify the signal which has weakened somewhat by the time it reaches the station. The amplified signals are then relayed towards their destination and may encounter several other repeater stations on the way. 4/ Fibre Optics in Medicine Optic fibres are used in medicine in endoscopes. The main part of an endoscope is the optical fibre. Light is shone down the optical fibre and a medical doctor can use the endoscope to look inside a patient. Endoscopes are used to examine the inside of a patient’s stomach, by inserting the endoscope down the patient’s throat. Endoscopes allow minimally invasive surgery. This means that a person can be diagnosed and treated through a small incision. This has advantages over open surgery because endoscopy is quicker and cheaper and the patient recovers more quickly. The alternative is open surgery which is expensive, requires more time and is more traumatic for the patient. Xem thêm: Physics 10.VI Geometrical Optics High School Students Studying the Sciences Physics