Optics 3 - Critical Angle and Total Internal Reflection PDF

7.4 Optics 7.4.4 Total Internal Reflection Critical Angle and Total Internal Reflection Consider light passing from a dense to a rare medium e.g. from water to air. The ray of light will be refracted away from the normal as can be seen in figure 10. Air...

7.4 Optics 7.4.4 Total Internal Reflection Critical Angle and Total Internal Reflection Consider light passing from a dense to a rare medium e.g. from water to air. The ray of light will be refracted away from the normal as can be seen in figure 10. Air 𝑐° 𝑖° 𝑖° Water Angle of incidence = 0°. Angle of incidence Angle of incidence Angle of incidence is less than the is equal to the is greater than the critical angle. critical angle. The critical angle. Total Refraction occurs. light is refracted internal reflection along the boundary. occurs. Figure 10 The same happens when light passes from glass to air (from a denser medium to a less dense medium). The light refracts away from the normal. Air Rare 𝑟° 𝑟° medium (less 𝑖° 𝑖° 𝑐° 𝑐° 𝑖° 𝑖° Dense dense) Glass medium (denser) Refraction Critical angle Total internal reflection 𝑖° < 𝑐° 𝑖° = 𝑐° 𝑖° > 𝑐° A B C Figure 11 L. BONELLO 14 7.4 Optics Critical Angle The critical angle is the angle of incidence in the denser medium such that the refracted ray grazes along the boundary, making an angle of refraction of 𝟗𝟎°. Total Internal Reflection Total internal reflection occurs when all the incident light is reflected inside the optically denser medium. No refraction occurs. Conditions for Total Internal Reflection 1. The incident ray must pass from an optically denser medium to an optically less dense medium. 2. The angle of incidence must be greater than the critical angle. Applying Snell’s Law to figure 11 B: 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2 …Equation 1 𝑛1 sin 𝑐 = 1 sin 90° where 𝑛2 = 1, the refractive index of air 𝑛1 sin 𝑐 = 1 1 𝑛1 = sin 𝑐 L. BONELLO 15 7.4 Optics The above equation is only used when the second medium is air. Also, from Equation 1: Bringing sin 𝜃1 subject of the formula, 𝑛2 sin 𝜃1 = sin 𝜃2 𝑛1 𝑛2 i.e. sin 𝑐 = sin 90° 𝑛1 𝑛2 sin 𝑐 =.1 𝑛1 𝑛2 sin 𝑐 = 𝑛1 where: 𝑛1 = Refractive index of denser medium (𝑁𝑜 𝑢𝑛𝑖𝑡𝑠) 𝑛2 = Refractive index of less dense medium (𝑁𝑜 𝑢𝑛𝑖𝑡𝑠) This equation is used for any pair of media. E.g. Light travels from glass to water as shown in figure 12. Find the critical angle. From denser to rarer medium: refracted ray bends away from the normal 𝑛 = 1.33 Water 90° (Less Dense medium) 𝑛 = 1.5 Glass (Denser medium) Figure 12 L. BONELLO 16 7.4 Optics Applying Snell’s Law: 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2 1.5 sin 𝑐 = 1.33 sin 90° 1.33 𝑥 1 sin 𝑐 = 1.5 sin 𝑐 = 0.8867 𝑐 = sin−1 (0.8867) ∴ 𝑐 = 62.5° Total Internal Reflection in a Prism A B C Figure 13 In figure 13, the ray of light travels straight ahead at A as it is exactly on the normal and so travels at 90° to the glass surface at A. The ray of light then hits the glass/air boundary at B at an angle of incidence of 45°. This angle is greater than the critical angle for glass, which is 42°. Therefore, no refraction takes place but all the light is totally internally reflected. Again, at C, the light is travelling along the normal and so travels straight through from glass to air. In this way, light has deviated through 90° due to total internal reflection. L. BONELLO 17 7.4 Optics Natural Phenomenon due to Total Internal Reflection 1. Mirage: A mirage is an optical illusion. E.g. On a hot summer day, on a stretch of road, there will be multiple layers of air with different temperatures and so different refractive indices. When the sun is at a certain angle, it will refract through these layers until total internal reflection takes place. The light bends as can be seen in figures 14 and 15. Figure 14 L. BONELLO 18 7.4 Optics Figure 15 2. Optic Fibres: These are communication systems which transmit signals by total internal reflection. Light is reflected at the core-cladding boundary and is trapped inside the core. Figure 16 L. BONELLO 19  7.4 Optics 3. Light under Water Light under water, beneath the sea, reflects internally as the sea is optically denser than the air. Normal Air (less dense medium - gas) where 𝜃 > 𝑐 𝜃 𝜃 Water (denser medium - liquid) Total internal reflection Figure 17 4. Cats’ Eyes: Cats’ eyes shine due to total internal reflection. The light enters their eyes at an angle greater than the critical angle. For this reason, the light rays are reflected, making their eyes seem like they are shining. 5. Rainbow: The rainbow is caused by light on raindrops reflecting internally and breaking up into colours. Figure 18 L. BONELLO 20  7.4 Optics Step-Index Fibres These transmit telephone signals and cable television signals. E.g. In the figure below, the core of an optical fibre has a refractive index of 1.6 while the cladding has a refractive index of 1.5. A ray PQ in air is incident at an angle 𝑖. The refracted ray QR is then incident at the critical angle 𝑐 on the core/cladding boundary. Calculate the angle 𝑖. Air n = 1 Cladding n = 1.5 90° R 𝑐 𝑐 Q 𝑟 Core n = 1.6 𝑖 Cladding n = 1.5 P Figure 19 Applying Snell’s Law: At R: 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2 1.6 sin 𝑐 = 1.5 sin 90° 1.5 𝑥 1 sin 𝑐 = 1.6 sin 𝑐 = 0.9375 𝑐 = sin−1 (0.9375) 𝑐 = 69.6° L. BONELLO 21 7.4 Optics At Q: 𝑐 + 𝑟 = 90° 𝑟 = 90° − 𝑐 𝑟 = 90° − 69.6° 𝑟 = 20.4° Applying Snell’s Law: At Q: 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2 1 𝑥 sin 𝑖 = 1.6 sin 20.4° 1.6 𝑥 0.3486 sin 𝑖 = 1 sin 𝑖 = 0.5578 𝑖 = sin−1 (0.5578) ∴ 𝑖 = 33.9° L. BONELLO 22