CLASS XI - Chapter 9 optics (MAHARASHRA STATE BOARD)
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This document provides an overview of optics and concepts related to reflection and refraction of light, including: - Dispersion of light occurs due to the refractive index and wavelength of light. Total internal reflection occurs when light travels from an optically dense medium to a less dense one at an angle greater than the critical angle. - Reflection and refraction follow specific laws when light interacts with plane and curved surfaces. Multiple images can form when light reflects between two mirrors. - Refractive index is the ratio of light speeds in different media and determines how much light bends when passing from one medium to another. Optical fibers use total internal reflection to transmit light signals with low loss.
CLASS XI - Chapter 9 optics (MAHARASHRA STATE BOARD)
- 1. Std : 11th Year : 2020-21 Subject : PHYSICS CHAPTER 9 : OPTICS MAHARASHTRA STATE BOARD
- 2. CAN YOU RECALL? • What are laws of reflection and refraction? • What is dispersion of light? Dispersion of light is the splitting of white light into its constituent colors due to the refractive index of the surface and the wavelength of the light. • What is refractive index? The ratio of the velocity of light in a vacuum to its velocity in a specified medium.
- 3. CAN YOU RECALL? • What is total internal reflection? Total internal reflection is the phenomenon of bouncing back of light in the same medium after striking the boundary of a rarer medium. • How does light refract at a curved surface? When the ray falls on any. point it makes some angle with normal and following law of reflection the reflected ray make equal angle with normal as incident ray goes backward. • How does a rainbow form? When sunlight hits a rain droplet, some of the light is reflected. The electromagnetic spectrum is made of light with many different wavelengths, and each is reflected at a different angle.
- 4. 9.1 Introduction • “See it to believe it” is a popular saying. • In order to see, we need light. • What exactly is light and how are we able to see anything? • We know that acoustics is the term used for science of sound. • Similarly, optics is the term used for science of light. • There is a difference in the nature of sound waves and light waves.
- 5. 9.4 REFLECTION 9.4.1 Reflection from a plane surface: a) If the object is in front of a plane reflecting surface, the image is virtual and laterally inverted. b) If we are standing on the bank of a still water body and look for our image formed by water, the image is laterally reversed, of the same size and on the other side. c) If an object is kept between two plane mirrors inclined at an angle 𝜃 (like in a kaleidoscope), a number of images are formed due to multiple reflections from both the mirrors.
- 6. 9.4 REFLECTION 9.4.1 Reflection from a plane surface 𝑛 = 360 𝜃 Let N be the number of images seen. I. If n is an even integer, 𝑁 = (𝑛 − 1), irrespective of where the object is. II. If n is an odd integer and object is exactly on the angle bisector, 𝑁 = 𝑛 − 1 . III. If n is an odd integer and object is off the angle bisector, 𝑁 = 𝑛 IV. If 𝑛 is not an integer, 𝑁 = 𝑚, where 𝑚 is integral part of 𝑛.
- 7. • Find number of images formed according to given case (a) 8, 9 (b) 9, 8 (c) 8, 8 (d) 9, 9 Ans: The number of images formed in two plane mirrors inclined at an angle A to each other is given by the below formula. Number of images n = 360/A – 1 The number of images formed n = (360/A)-1, if (360/A) is even integer. If (360/A) is odd integer, the number of images formed n = (360/A)-1 when the object is kept symmetrically, and n = (360/A) when object is kept asymmetrically. If (360/A) is a fraction, the number of images formed is equal to its integral part. As the angle gets smaller (down to 0 degrees when the mirrors are facing each other and parallel) the smaller the angle the greater the number of images. Here, the angle A between the mirrors is 40 degrees. Case (a): The object is symmetrically placed. The number of images formed = (360/40)-1, we get 8 images. Case (b): The object is asymmetrically placed. The number of images formed = (360/40), we get 9 images. Hence, the number of images formed are 8 and 9 respectively.
- 8. Example: A small object is kept symmetrically between two plane mirrors inclined at 380. This angle is now gradually increased to 410, the object being symmetrical all the time. Determine the number of images visible during the process. Solution: According to the convention used in the table above, 𝜃 = 380 ∴ 𝑛 = 360 38 = 9.47 ∴ 𝑁 = 9 This is valid till the angle is 400 as the object is kept symmetrically Beyond 400, n > 9 and it decreases upto 360 41 = 8.78. Hence now onwards there will be 8 images till 410.
- 9. If a ray of light comes to an interface between two media and enters into another medium of different refractive index, it changes itself suitable to that medium. This phenomenon is defined as refraction of light. Absolute refractive index: Absolute refractive index of a medium is the ratio of speed of light in vacuum to that in the given medium. 𝑛 = 𝑐 𝑣 Medium having greater value of n is called optically denser. Relative refractive index: 9.5 Refraction
- 10. Do you know ? (a) Logic behind the convention 2 1 𝑛: Letter n is the symbol for refractive index, 𝑛2 corresponds to refractive index of medium 2 and 2 1 𝑛 indicates that it is with respect to medium 1. In this case, light travels from medium 1 to 2 so we need to discuss medium 2 in context to medium 1. (b) Dictionary meaning of the word refract is to change the path. However, in context of Physics, we should be more specific. We use the word deviate for changing the path. During refraction at normal incidence, there is no change in path. Thus, there is refraction but no deviation. Deviation is associated with refraction only during oblique incidence. Deviation or changing the path or bending is associated with many phenomena such as reflection, diffraction, scattering, gravitational bending due to a massive object, etc.
- 11. Illustrations of refraction: 1) 𝑛𝑤𝑎𝑡𝑒𝑟 ≅ 𝑅𝑒𝑎𝑙 𝑑𝑒𝑝𝑡ℎ 𝑎𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ tan 𝑟 = 𝑥 𝐴 ≅ sin(𝑟) and tan 𝑖 = 𝑥 𝑅 ≅ sin(𝑖) ∴ 𝑛 = sin(𝑟) sin(𝑖) = 𝑥 𝐴 𝑥 𝑅 = 𝑅 𝐴 ∴ 𝑛 = 𝑅𝑒𝑎𝑙 𝑑𝑒𝑝𝑡ℎ 𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ 2) A stick or pencil kept obliquely in a glass containing water appears broken as its part in water appears to be raised. 9.5 Refraction Fig.: Real and apparent depth.
- 12. Small angle approximation: For small angles, expressed in radian, sin 𝜃 ≅ 𝜃 ≅ tan 𝜃 For example, for 𝜃 = 300 = 𝜋 6 𝑐 = 0.5236𝑐, We have sin 𝜃 = 0.5 In this case the error is 0.5236 − 0.5 = 0.0236 in 0.5, which is 4.72 %. For practical purposes we consider angles less than 100 where the error in using sin 𝜃 ≅ 𝜃 is less than 0.51 %. (Even for 600, it is still 15.7 %) It is left to you to verify that this is almost equally valid for tan 𝜃 till 200 only. 9.5 Refraction
- 13. Example: A crane flying 6 m above a still, clear water lake sees a fish underwater. For the crane, the fish appears to be 6 cm below the water surface. How much deep should the crane immerse its beak to pick that fish? For the fish, how much above the water surface does the crane appear? Refractive index of water 4/3. Solution: For crane, apparent depth of the fish is 6 cm and real depth is to be determined. For fish, real depth (height, in this case) of the crane is 6 m and apparent depth (height) is to be determined. 𝑛 = 𝑅 𝐴 = 𝑅𝑒𝑎𝑙 𝑑𝑒𝑝𝑡ℎ 𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ For crane, it is water with respect to air as real depth is in water and approve depth is as seen from air ∴ 𝑛 = 4 3 = 𝑅 𝐴 = 𝑅 6 𝑅 = 8 𝑐𝑚 For fish, it is air with respect to water as the real height is in air and seen from water. ∴ 𝑛 = 3 4 = 𝑅 𝐴 = 6 𝐴 𝐴 = 8 𝑚
- 14. • For angles of incidence greater than 𝑖𝑐, the angle of refraction become larger than 900 and the ray does not enter into rarer medium at all but is reflected totally into the denser medium. This is called total internal reflection. • During total internal reflection TIR, it is total reflection and no refraction. • The corresponding angle of incidence in the denser medium is greater than or equal to the critical angle. 9.6 Total internal reflection Fig.: Total internal reflection. • Critical angle for a pair of refracting media can be defined as that angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 900. sin 𝑖𝑐 = 1 𝜇 𝜇 sin 𝑖𝑐 = 1 sin 900 • For commonly used glasses of 𝜇 = 1.5, 𝑖𝑐 = 41049′ ≅ 420 𝑎𝑛𝑑 𝑓𝑜𝑟 𝑤𝑎𝑡𝑒𝑟 𝑜𝑓 𝜇 = 4 3 , 𝑖𝑐 = 48035′ (𝐵𝑜𝑡ℎ, 𝑤𝑖𝑡ℎ 𝑟𝑒𝑠𝑝𝑒𝑐𝑡 𝑡𝑜 𝑎𝑖𝑟)
- 15. Do you know ? In Physics the word critical is used when certain phenomena are not applicable or more than one phenomenon are applicable. Some examples are as follows. i. In case of total internal reflection, the phenomenon of reversibility of light is not applicable at critical angle and refraction is possible only for angles of incidence in the denser medium smaller than the critical angle. ii. At the critical temperature, a substance coexists into all the three states; solid, liquid and gas. iii. For liquids, streamline flow is possible till critical velocity is achieved.
- 16. 9.6 Total internal reflection 9.6.1 Applications of total internal reflection: I. Optical fibre: • An optical fibre essentially consists of an extremely thin (slightly thicker than a human hair), transparent, flexible core surrounded by optically rarer (smaller refractive index), flexible cover called cladding. • Entire thickness of the fibre is less than half a mm. (Fig.(a)). • An optical signal (ray) entering the core suffers multiple total internal reflections (Fig.(b)) & emerges after several kilometers with extremely low loss travelling with highest possible speed in that material (~ 2,00,000 km/s for glass). Fig. (a): Optical fibre construction. Fig. (b): Optical fibre working.
- 17. 9.6 Total internal reflection 9.6.1 Applications of total internal reflection: Some of the advantages of optic fibre communication are listed below. a) Broad bandwidth (frequency range) b) Immune to EM interference c) Low attenuation loss d) Electrical insulator e) Theft prevention f) Security of information Fig. (a): Optical fibre construction. Fig. (b): Optical fibre working.