Physics 2 PDF Past Paper

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This principle marks a departure from the legacy of bookish learning which continues to shape our system and causes a gap between the school, home and community. The syllabi and textbooks developed on the basis of NCF signify an attempt to implement this basic idea. They also attempt to discourage rote learning and the maintenance of sharp boundaries between different subject areas. We hope these measures will take us significantly further in the direction of a child-centred system of education outlined in the National Policy on Education (NPE), 1986. The success of this effort depends on the steps that school principals and teachers will take to encourage children to reflect on their own learning and to pursue imaginative activities and questions. We must recognise that, given space, time and freedom, children generate new knowledge by engaging with the information passed on to them by adults. Treating the prescribed textbook as the sole basis of examination is one of the key reasons why other resources and sites of learning are ignored. Inculcating creativity and initiative is possible if we perceive and treat children as participants in learning, not as receivers of a fixed body of knowledge. These aims imply considerable change in school routines and mode of functioning. Flexibility in the daily time-table is as necessary as rigour in implementing the annual calendar so that the required number of teaching days are actually devoted to teaching. The methods used for teaching and evaluation will also determine how effective this textbook proves for making children’s life at school a happy experience, rather than a source of stress or boredom. Syllabus designers have tried to address the problem of curricular burden by restructuring and reorienting knowledge at different stages with greater consideration for child psychology and the time available for teaching. The textbook attempts to enhance this endeavour by giving higher priority and space to opportunities for contemplation and wondering, discussion in small groups, and activities requiring hands-on experience. The National Council of Educational Research and Training (NCERT) appreciates the hard work done by the textbook development committee responsible for this book. We wish to thank the Chairperson of the advisory group in science and mathematics, Professor J.V. Narlikar and the Chief Advisor for this book, Professor A.W. Joshi for guiding the work of this committee. Several teachers contributed to the development of this textbook; we are grateful to their principals for making this possible. We are indebted to the institutions and organisations which have generously permitted us to draw upon their resources, material and personnel. We are especially grateful to the members of the National Monitoring Committee, appointed by the Department of Secondary and Higher Education, Ministry of Human Resource Development under the Chairpersonship of Professor Mrinal Miri and Professor G.P. Deshpande, for their valuable time and contribution. As an organisation committed to systemic reform and continuous improvement in the quality of its products, NCERT welcomes comments and suggestions which will enable us to undertake further revision and refinement. Director New Delhi National Council of Educational 20 November 2006 Research and Training  PREFACE It gives me pleasure to place this book in the hands of the students, teachers and the public at large (whose role cannot be overlooked). It is a natural sequel to the Class XI textbook which was brought out in 2006. This book is also a trimmed version of the textbooks which existed so far. The chapter on thermal and chemical effects of current has been cut out. This topic has also been dropped from the CBSE syllabus. Similarly, the chapter on communications has been substantially curtailed. It has been rewritten in an easily comprehensible form. Although most other chapters have been based on the earlier versions, several parts and sections in them have been rewritten. The Development Team has been guided by the feedback received from innumerable teachers across the country. In producing these books, Class XI as well as Class XII, there has been a basic change of emphasis. Both the books present physics to students without assuming that they would pursue this subject beyond the higher secondary level. This new view has been prompted by the various observations and suggestions made in the National Curriculum Framework (NCF), 2005. Similarly, in today’s educational scenario where students can opt for various combinations of subjects, we cannot assume that a physics student is also studying mathematics. Therefore, physics has to be presented, so to say, in a stand-alone form. As in Class XI textbook, some interesting box items have been inserted in many chapters. They are not meant for teaching or examinations. Their purpose is to catch the attention of the reader, to show some applications in daily life or in other areas of science and technology, to suggest a simple experiment, to show connection of concepts in different areas of physics, and in general, to break the monotony and enliven the book. Features like Summary, Points to Ponder, Exercises and Additional Exercises at the end of each chapter, and Examples have been retained. Several concept-based Exercises have been transferred from end-of-chapter Exercises to Examples with Solutions in the text. It is hoped that this will make the concepts discussed in the chapter more comprehensible. Several new examples and exercises have been added. Students wishing to pursue physics further would find Points to Ponder and Additional Exercises very useful and thoughtful. To provide resources beyond the textbook and to encourage eLearning, each chapter has been provided with some relevant website addresses under the title ePhysics. These sites provide additional materials on specific topics and also provide learners the opportunites for interactive demonstrations/ experiments. The intricate concepts of physics must be understood, comprehended and appreciated. Students must learn to ask questions like ‘why’, ‘how’, ‘how do we know it’. They will find almost always that the question ‘why’ has no answer within the domain of physics and science in general. But that itself is a learning experience, is it not? On the other hand, the question ‘how’ has been reasonably well answered by physicists in the case of most natural phenomena. In fact, with the understanding of how things happen, it has been possible to make use of many phenomena to create technological applications for the use of humans.  For example, consider statements in a book, like ‘A negatively charged electron is attracted by the positively charged plate’, or ‘In this experiment, light (or electron) behaves like a wave’. You will realise that it is not possible to answer ‘why’. This question belongs to the domain of philosophy or metaphysics. But we can answer ‘how’, we can find the force acting, we can find the wavelength of the photon (or electron), we can determine how things behave under different conditions, and we can develop instruments which will use these phenomena to our advantage. It has been a pleasure to work for these books at the higher secondary level, along with a team of members. The Textbook Development Team, the Review Team and Editing Teams involved college and university teachers, teachers from Indian Institutes of Technology, scientists from national institutes and laboratories, as well as higher secondary teachers. The feedback and critical look provided by higher secondary teachers in the various teams are highly laudable. Most box items were generated by members of one or the other team, but three of them were generated by friends and well-wishers not part of any team. We are thankful to Dr P.N. Sen of Pune, Professor Roopmanjari Ghosh of Delhi and Dr Rajesh B Khaparde of Mumbai for allowing us to use their box items, respectively in Chapters 3, 4 (Part I) and 9 (Part II). We are very thankful to the members of the Review and Editing Workshops to discuss and refine the first draft of the textbook. We also express our gratitude to Prof. Krishna Kumar, Director, NCERT, for entrusting us with the task of presenting this textbook as a part of the national effort for improving science education. I also thank Prof. G. Ravindra, Joint Director, NCERT, for his help from time-to-time. Prof. Hukum Singh, Head, Department of Education in Science and Mathematics, NCERT, was always willing to help us in our endeavour in every possible way. We welcome suggestions and comments from our valued users, especially students and teachers. We wish our young readers a happy journey into the exciting realm of physics. A. W. JOSHI Chief Advisor Textbook Development Committee  TEXTBOOK DEVELOPMENT COMMITTEE CHAIRPERSON, ADVISORY COMMITTEE FOR TEXTBOOKS IN SCIENCE AND MATHEMATICS J.V. Narlikar, Emeritus Professor, Inter-University Centre for Astronomy and Astrophysics (IUCAA), Ganeshkhind, Pune University Campus, Pune CHIEF ADVISOR A.W. Joshi, Honorary Visiting Scientist, National Centre for Radio Astrophysics (NCRA), Pune University Campus, Pune (Formerly Professor at Department of Physics, University of Pune) MEMBERS A.K. Ghatak, Emeritus Professor, Department of Physics, Indian Institute of Technology, New Delhi Alika Khare, Professor, Department of Physics, Indian Institute of Technology, Guwahati Anjali Kshirsagar, Reader, Department of Physics, University of Pune, Pune Anuradha Mathur, PGT , Modern School, Vasant Vihar, New Delhi Atul Mody, Lecturer (S.G.), VES College of Arts, Science and Commerce, Mumbai B.K. Sharma, Professor, DESM, NCERT, New Delhi Chitra Goel, PGT, Rajkiya Pratibha Vikas Vidyalaya, Tyagraj Nagar, New Delhi Gagan Gupta, Reader, DESM, NCERT, New Delhi H.C. Pradhan, Professor, Homi Bhabha Centre of Science Education (TIFR), Mumbai N. Panchapakesan, Professor (Retd.), Department of Physics and Astrophysics, University of Delhi, Delhi R. Joshi, Lecturer (S.G.), DESM, NCERT, New Delhi S.K. Dash, Reader, DESM, NCERT, New Delhi S. Rai Choudhary, Professor, Department of Physics and Astrophysics, University of Delhi, Delhi S.K. Upadhyay, PGT, Jawahar Navodaya Vidyalaya, Muzaffar Nagar S.N. Prabhakara, PGT, DM School, Regional Institute of Education (NCERT), Mysore V.H. Raybagkar, Reader, Nowrosjee Wadia College, Pune Vishwajeet Kulkarni, Teacher (Grade I ), Higher Secondary Section, Smt. Parvatibai Chowgule College, Margao, Goa MEMBER-COORDINATOR V.P. Srivastava, Reader, DESM, NCERT, New Delhi  Constitution of India Part IV A (Article 51 A) Fundamental Duties It shall be the duty of every citizen of India — (a) to abide by the Constitution and respect its ideals and institutions, the National Flag and the National Anthem; (b) to cherish and follow the noble ideals which inspired our national struggle for freedom; (c) to uphold and protect the sovereignty, unity and integrity of India; (d) to defend the country and render national service when called upon to do so; (e) to promote harmony and the spirit of common brotherhood amongst all the people of India transcending religious, linguistic and regional or sectional diversities; to renounce practices derogatory to the dignity of women; (f) to value and preserve the rich heritage of our composite culture; (g) to protect and improve the natural environment including forests, lakes, rivers, wildlife and to have compassion for living creatures; (h) to develop the scientific temper, humanism and the spirit of inquiry and reform; (i) to safeguard public property and to abjure violence; (j) to strive towards excellence in all spheres of individual and collective activity so that the nation constantly rises to higher levels of endeavour and achievement; *(k) who is a parent or guardian, to provide opportunities for education to his child or, as the case may be, ward between the age of six and fourteen years. Note: The Article 51A containing Fundamental Duties was inserted by the Constitution (42nd Amendment) Act, 1976 (with effect from 3 January 1977). *(k) was inserted by the Constitution (86th Amendment) Act, 2002 (with effect from 1 April 2010).  ACKNOWLEDGEMENTS The National Council of Educational Research and Training acknowledges the valuable contribution of the individuals and organisations involved in the development of Physics Textbook for Class XII. The Council also acknowledges the valuable contribution of the following academics for reviewing and refining the manuscripts of this book: Anu Venugopalan, Lecturer, School of Basic and Applied Sciences, GGSIP University, Delhi; A.K. Das, PGT, St. Xavier’s Senior Secondary School, Delhi; Bharati Kukkal, PGT, Kendriya Vidyalaya, Pushp Vihar, New Delhi; D.A. Desai, Lecturer (Retd.), Ruparel College, Mumbai; Devendra Kumar, PGT, Rajkiya Pratibha Vikas Vidyalaya, Yamuna Vihar, Delhi; I.K. Gogia, PGT, Kendriya Vidyalaya, Gole Market, New Delhi; K.C. Sharma, Reader, Regional Institute of Education (NCERT), Ajmer; M.K. Nandy, Associate Professor, Department of Physics, Indian Institute of Technology, Guwahati; M.N. Bapat, Reader, Regional Institute of Education (NCERT), Mysore; R. Bhattacharjee, Asstt. Professor, Department of Electronics and Communication Engineering, Indian Institute of Technology, Guwahati; R.S. Das, Vice-Principal (Retd.), Balwant Ray Mehta Senior Secondary School, Lajpat Nagar, New Delhi; Sangeeta D. Gadre, Reader, Kirori Mal College, Delhi; Suresh Kumar, PGT, Delhi Public School, Dwarka, New Delhi; Sushma Jaireth, Reader, Department of Women’s Studies, NCERT, New Delhi; Shyama Rath, Reader, Department of Physics and Astrophysics, University of Delhi, Delhi; Yashu Kumar, PGT, Kulachi Hans Raj Model School, Ashok Vihar, Delhi. The Council also gratefully acknowledges the valuable contribution of the following academics for the editing and finalisation of this book: B.B. Tripathi, Professor (Retd.), Department of Physics, Indian Institute of Technology, New Delhi; Dipan K. Ghosh, Professor, Department of Physics, Indian Institute of Technology, Mumbai; Dipanjan Mitra, Scientist, National Centre for Radio Astrophysics (TIFR), Pune; G.K. Mehta, Raja Ramanna Fellow, Inter-University Accelerator Centre, New Delhi; G.S. Visweswaran, Professor, Department of Electrical Engineering, Indian Institute of Technology, New Delhi; H.C. Kandpal, Head, Optical Radiation Standards, National Physical Laboratory, New Delhi; H.S. Mani, Raja Ramanna Fellow, Institute of Mathematical Sciences, Chennai; K. Thyagarajan, Professor, Department of Physics, Indian Institute of Technology, New Delhi; P.C. Vinod Kumar, Professor, Department of Physics, Sardar Patel University, Vallabh Vidyanagar, Gujarat; S. Annapoorni, Professor, Department of Physics and Astrophysics, University of Delhi, Delhi; S.C. Dutta Roy, Emeritus Professor, Department of Electrical Engineering, Indian Institute of Technology, New Delhi; S.D. Joglekar, Professor, Department of Physics, Indian Institute of Technology, Kanpur; V. Sundara Raja, Professor, Sri Venkateswara University, Tirupati. The Council also acknowledges the valuable contributions of the following academics for refining the text in 2017: A.K. Srivastava, Assistant Professor, DESM, NCERT, New Delhi; Arnab Sen, Assistant Professor, NERIE, Shillong; L.S. Chauhan, Assistant Professor, RIE, Bhopal; O.N. Awasthi, Professor (Retd.), RIE, Bhopal; Rachna Garg, Professor, DESM, NCERT, New Delhi; Raman Namboodiri, Assistant Professor, RIE, Mysuru; R.R. Koireng, Assistant Professor, DCS, NCERT, New Delhi; Shashi Prabha, Professor, DESM, NCERT, New Delhi; and S.V. Sharma, Professor, RIE, Ajmer. Special thanks are due to Hukum Singh, Professor and Head, DESM, NCERT for his support. The Council also acknowledges the support provided by the APC office and the administrative staff of the DESM; Deepak Kapoor, Incharge, Computer Station; Inder Kumar, DTP Operator; Mohd. Qamar Tabrez and Hari Darshan Lodhi Copy Editor ; Rishi Pal Singh, Sr. Proof Reader, NCERT and Ashima Srivastava, Proof Reader in shaping this book. The contributions of the Publication Department in bringing out this book are also duly acknowledged.  ˛õòyÌ≈!Óòƒy å˲yàÈüÈ1äÈüÈ~Ó˚ §)!ã˛˛õe myò¢ ˆ◊!î ≤ÃÌÙ xôƒyÎ˚ ï˛!í˛¸Í xyôyl ~ÓÇ ˆ«˛e 1 !mï˛#Î˚ xôƒyÎ˚ !fiÌÓ˚ ï˛!í˛¸Í !ÓË˛Ó ~ÓÇ ôyÓ˚ܲc 51 ï,˛ï˛#Î˚ xôƒyÎ˚ ≤ÃÓy # ï˛!í˛¸Í 93 ã˛ï%˛Ì≈ xôƒyÎ˚ ≤ÃÓy # xyôyl G ã%˛¡∫ܲc 132 ˛õM˛Ù xôƒyÎ˚ ã%˛¡∫ܲc ~ÓÇ ˛õòyÌ≈ 173 £Ï¤˛ xôƒyÎ˚ ï˛!í˛¸Í ã%˛¡∫ܲ#Î˚ xyˆÏÓ¢ 204 §ÆÙ xôƒyÎ˚ ˛õ!Ó˚Óï≈˛# ≤ÃÓy 233 xT˛Ù xôƒyÎ˚ ï˛!í˛¸Íã%˛¡∫ܲ#Î˚ ï˛Ó˚Aà 269 í˛z_Ó˚Ùy°y 288  §)!ã˛˛õe lÓÙ xôƒyÎ˚ Ó˚!Ÿ¬ xyˆÏ°yܲ !ÓK˛yl ~ÓÇ xyˆÏ°yܲ#Î˚ Îsfy!ò 9.1 Ë)˛!Ùܲy 309 9.2 ˆày°#Î˚ ò˛õ≈î myÓ˚y xyˆÏ°yÓ˚ ≤Ã!ï˛Ê˛°l 310 9.3 ≤Ã!ï˛§Ó˚î 316 9.4 x˲ƒhs˝Ó˚#î ˛õ)î≈ ≤Ã!ï˛Ê˛°l 319 9.5 ˆày°#Î˚ ï˛ˆÏ° ~ÓÇ ˆ°ˆÏ™ ≤Ã!ï˛§Ó˚î 323 9.6 !≤ÃçˆÏÙÓ˚ Ùôƒ !òˆÏÎ˚ ≤Ã!ï˛§Ó˚î 330 9.7 !≤ÃçÙ myÓ˚y !ÓFS%ÈÓ˚î 332 9.8 §)Î≈yˆÏ°yܲ ç!lï˛ Ü˛ˆÏÎ˚ܲ!ê˛ ≤ÃyÜ,˛!ï˛Ü˛ âê˛ly 333 9.9 xyˆÏ°yܲ#Î˚ Îsf§Ù) 335 ò¢Ù xôƒyÎ˚ ï˛Ó˚Aà xyˆÏ°yܲ !ÓK˛yl 10.1 Ë)˛!Ùܲy 351 10.2 y zˆÏàl‰ˆÏ§Ó˚ l#!ï˛ 353 10.3 y zˆÏàl‰ˆÏ§Ó˚ l#!ï˛ ≤ÈÏÎ˚yˆÏà §Ùï˛° ï˛Ó˚ˆÏAàÓ˚ ≤Ã!ï˛§Ó˚î ~ÓÇ ≤Ã!ï˛Ê˛°l 355 10.4 §%§Çàï˛ ~ÓÇ x§Çàï˛ ï˛Ó˚ˆÏAàÓ˚ §ÇˆÏÎyçl 360 10.5 xyˆÏ°yܲ ï˛Ó˚ˆÏAàÓ˚ Óƒ!ï˛ã˛yÓ˚ ~ÓÇ zÎ˚ÇÈüÈ~Ó˚ ˛õÓ˚#«˛y 362 10.6 x˛õÓï≈˛l 367 10.7 §ÙÓï≈˛l 376 ~ܲyò¢ xôƒyÎ˚ !Ó!ܲÓ˚î ~ÓÇ ˛õòyˆÏÌ≈Ó˚ ˜mï˛ ≤ÃÜ,˛!ï˛ 11.1 Ë)˛!Ùܲy 386 11.2 zˆÏ°Ü˛ê˛∆l !l/§Ó˚î 387 11.3 xyˆÏ°yܲï˛!í˛¸Í !ܲÎ˚y 388 11.4 xyˆÏ°yܲ ï˛!í˛¸Í!ܲÎ˚yÓ˚ ˛õÓ˚#«˛yÙ)°Ü˛ xôƒÎ˚l 389 11.5 xyˆÏ°yܲ ï˛!í˛¸Í !ܲÎ˚y ~ÓÇ xyˆÏ°yÓ˚ ï˛Ó˚Aà ï˛_¥ 393 11.6 xy zlfiê˛y zˆÏlÓ˚ xyˆÏ°y ï˛!í˛¸Í §Ù#ܲÓ˚î 393 11.7 xyˆÏ°yÓ˚ ܲîy ≤ÃÜ,˛!ï˛ ı ˆÊ˛yê˛l 395 11.8 ˛õòyˆÏÌ≈Ó˚ ï˛Ó˚Aà ≤ÃÜ,˛!ï˛ 398 11.9 ˆí˛!˲§l ~ÓÇ àyÙ≈yÓ˚ ˛õÓ˚#«˛y 403 myò¢ xôƒyÎ˚ ˛õÓ˚Ùyî%§Ù) 12.1 Ë)˛!Ùܲy 414 12.2 xy°Ê˛yÈüÈܲîyÓ˚ !ӈϫ˛˛õî ~ÓÇ ˛õÓ˚Ùyî%Ó˚ Ó˚yòyÓ˚ˆÏÊ˛yˆÏí≈˛Ó˚ !lí˛z!Üœ˛Î˚ ÙˆÏí˛° 415 12.3 ˛õyÓ˚Ùyî!Óܲ Óî≈y!° 420 12.4 y zˆÏí»˛yˆÏçl ˛õÓ˚Ùyî% §¡õ!Ü≈˛ï˛ ˆÓyÓ˚ ÙˆÏí˛° 422 12.5 y zˆÏí»˛yˆÏçl ˛õÓ˚Ùyî%Ó˚ ˆÓ˚áy Óî≈y!° 428 12.6 !í˛ÈüÈÓà!° myÓ˚y ˆÜ˛yÎ˚yrê˛yÎ˚l §Çܲyhs˝ ˆÓyˆÏÓ˚Ó˚ !mï˛#Î˚ fl∫#ܲyˆÏÎ≈Ó˚ Óƒyáƒy 430 eˆÏÎ˚yò¢ xôƒyÎ˚ !lí˛z!Üœ˛Î˚y§ Óy ˆÜ˛wܲ 13.1 Ë)˛!Ùܲy 438 13.2 ˛õÓ˚Ùyî%Ó˚ ˲Ó˚ ~ÓÇ !lí˛z!Üœ˛Î˚yˆÏ§Ó˚ àë˛l 439 13.3 !lí˛z!Üœ˛Î˚yˆÏ§Ó˚ xyܲyÓ˚ 441 13.4 ˲Ó˚ÈüÈ¢!=˛ ~ÓÇ !lí˛z!Üœ˛Î˚ Órôl ¢!=˛ 442 13.5 !lí˛z!Üœ˛Î˚ Ó° 445 13.6 ˆï˛ç!fl;Î˚ï˛y 446 13.7 !lí˛z!Üœ˛Î˚ ¢!=˛ 451 ã˛ï%˛ò≈¢ xôƒyÎ˚ xô≈˛õ!Ó˚Óy # zˆÏ°Ü˛ê˛∆!l: ı í˛z˛õyòyl ˛õòyÌ≈ñ Îsfy!ò ~ÓÇ §Ó˚° Óï≈˛l#§Ù) 14.1 Ë)˛!Ùܲy 467 14.2 ôyï%˛ñ ˛õ!Ó˚Óy # ~ÓÇ xô≈˛õ!Ó˚Óy #Ó˚ ˆ◊!î!Ólƒy§ 468 14.3 !Ó¢%Âô Óy fl∫ܲ#Î˚ xô≈˛õ!Ó˚Óy # 472 14.4 x!Ó¢%Âô xô≈˛õ!Ó˚Óy # 474 14.5 p-n §ÇˆÏÎyà 478 14.6 xô≈˛õ!Ó˚Óy # í˛yˆÏÎ˚yí˛ 479 14.7 ~ܲÙ%á#ܲyÓ˚ܲ ! ˆÏ§ˆÏÓ §ÇˆÏÎyà í˛yˆÏÎ˚yˆÏí˛Ó˚ ÓƒÓ yÓ˚ 483 14.8 !ӈϢ£Ï í˛zˆÏj¢ƒ§¡õߨ p-n §ÇˆÏÎyà í˛yˆÏÎ˚yí˛ 485 14.9 §ÇˆÏÎyà ê˛∆yl!çfiê˛yÓ˚ 490 14.10 !í˛!çê˛y° zˆÏ°Ü˛ê˛∆!l:ÈüÈ~ÓÇ °!çܲ ˆàê˛ 501 14.11 §Ù!ß∫ï˛ Óï≈˛l# 505 ˛õM˛ò¢ xôƒyÎ˚ ˆÎyàyˆÏÎyà ÓƒÓfiÌy 15.1 Ë)˛!Ùܲy 513 15.2 ˆÎyàyˆÏÎyà ÓƒÓfiÌy˛õlyÓ˚ í˛z˛õyòyl§Ù) 513 15.3 ˜Óò%ƒ!ï˛l ˆÎyàyˆÏÎyà ÓƒÓfiÌy˛õlyÎ˚ ÓƒÓ ,ï˛ ≤ÃyÌ!Ùܲ Ó˚y!¢à%ˆÏ°y 515 15.4 §ÇˆÏܲˆÏï˛Ó˚ ˛õ!ê˛ˆÏÓô 517 15.5 §M˛y°l ÙyôƒˆÏÙÓ˚ ˛õ!ê˛ˆÏÓô 518 15.6 ï˛!í˛¸Fã%˛¡∫ܲ#Î˚ ï˛Ó˚Aà§Ù)ˆÏ Ó˚ !ÓhflÏyÓ˚ 519 15.7 Ùí%˛ˆÏ°¢l ~ÓÇ ~Ó˚ ≤ÈÏÎ˚yçl#Î˚ï˛y 522 15.8 !ÓhflÏyÓ˚ Ùí%˛ˆÏ°¢l 524 15.9 !ÓhflÏyÓ˚ Ùí%˛ˆÏ°¢lÎ%=˛ ï˛Ó˚ˆÏAàÓ˚ í˛zͲõyòl 525 15.10 !ÓhflÏyÓ˚ Ùí˛%ˆÏ°¢lÎ%=˛ ï˛Ó˚ˆÏAàÓ˚ Ù)° §ÇˆÏÜ˛ï˛ §rôyl 526 ˛õ!Ó˚!¢T˛ 532 í˛z_Ó˚Ùy°y 534 BIBLIOGRAPHY 552 INDEX 554 lÓÙ xôƒyÎ˚ Ó˚!Ÿ¬ xyˆÏ°yܲ !ÓK˛yl ~ÓÇ xyˆÏ°yܲ#Î˚ Îsfy!ò (RAY OPTICS AND OPTICAL INSTRUMENTS) 9.1 Ë)˛!Ùܲy ≤ÃÜ,˛!ï˛ Ùyl%ˆÏ£ÏÓ˚ ˆã˛yˆÏá åˆÓ˚!ê˛lyä ï˛!í˛¸Í ã%˛¡∫ܲ#Î˚ Óî≈y°#Ó˚ ~ܲ «%˛o ˛õyÕ‘yÓ˚ ÙˆÏôƒ Ìyܲy ï˛!í˛¸Í ã%˛¡∫ܲ#Î˚ ï˛Ó˚Aàà%ˆÏ°yˆÏܲ § ˆÏç z ¢ly=˛ ܲÓ˚yÓ˚ «˛Ùï˛y ≤Ãòyl ܲˆÏÓ˚ˆÏSÈ– ï˛!í˛¸Íã%˛¡∫ܲ#Î˚ Óî≈y°#Ó˚ ~ z xM˛ˆÏ°Ó˚˛ åÎyˆÏòÓ˚ ï˛Ó˚Aà˜Ïòâ≈ƒ ≤ÃyÎ˚ 400 nm ˆÌˆÏܲ 750 nmä §Ç!Ÿ’T˛ !Ó!ܲÓ˚îˆÏܲ ÚxyˆÏ°yÜ˛Û ÓˆÏ°– Ù)°ï˛ xyˆÏ°y G ò¢≈ˆÏlÓ˚ xl%Ë)˛!ï˛Ó˚ ÙyôƒˆÏÙ z xyÙÓ˚y ã˛yÓ˚˛õyˆÏ¢Ó˚ !ÓŸªˆÏܲ çylˆÏï˛ G Óƒyáƒy ܲÓ˚ˆÏï˛ ˛õy!Ó˚– §yôyÓ˚î x!˲K˛ï˛y ˆÌˆÏܲ K˛ylï˛ xyÙÓ˚y xyˆÏ°yܲ §¡õˆÏÜ≈˛ ò%!ê˛ !Ó£ÏÎ˚ í˛zˆÏÕ‘á ܲÓ˚ˆÏï˛ ˛õy!Ó˚– ≤ÃÌÙï˛ñ xyˆÏ°y ï˛#Ó o%!ï˛ˆÏï˛ à!ï˛¢#° ~ÓÇ !mï˛#Î˚ï˛ñ ~!ê˛ §Ó˚°ˆÏÓ˚áyÎ˚ ã˛°yã˛° ܲˆÏÓ˚– xyˆÏ°yÓ˚ o%!ï˛ §§#Ù G ˛õ!Ó˚Ùy˛õˆÏÎyàƒñ ï˛y Ó%V˛ˆÏï˛ ˆÓ¢ !ܲS%È §ÙÎ˚ ˆ°ˆÏà!SÈ°– Óï≈˛ÙyˆÏl ¢)lƒ ÙyôƒˆÏÙ ~Ó˚ @˝Ã îˆÏÎyàƒ Ùyl c = 2.99792458 × 108 m s–1– x!ôܲyÇ¢ ˆ«˛ˆÏe ~Ó˚ §yÌ≈ܲ Ùyl c = 3 × 108 m s–1 ôÓ˚y Î˚– ¢)lƒ ÙyôƒˆÏÙ xyˆÏ°yÓ˚ o%!ï˛ z ° ≤ÃÜ,˛!ï˛ˆÏï˛ ≤ÃyÆ §ˆÏÓ≈yFã˛ o%!ï˛– xT˛Ù xôƒyˆÏÎ˚ xyÙÓ˚y ˆÎÙlê˛y !¢ˆÏá!SÈ ˆÎñ xyˆÏ°y ~ܲ!ê˛ ï˛!í˛¸Íã%˛¡∫ܲ#Î˚ ï˛Ó˚Aà ÎyÓ˚ ï˛Ó˚Aà˜Ïòâ≈ƒ Óî≈y°#Ó˚ ò,¢ƒÙyl xLjϢ xÓ!fiÌï˛ñ ~ z ï˛_¥!ê˛Ó˚ §yˆÏÌ xyˆÏ°yÓ˚ §Ó˚°˜ÏÓ˚!áܲ à!ï˛Ó˚ í˛z˛õ°kô ôyÓ˚îy!ê˛ !mÙï˛ ˆ˛õy£Ïî ܲˆÏÓ˚– ܲ#˲yˆÏÓ ~ ò%!ê˛Ó˚ ÙˆÏôƒ §yÙO§ƒ !Óôyl ܲÓ˚y ÎyÎ˚⁄ í˛z_Ó˚!ê˛ °ñ xyÙyˆÏòÓ˚ §ã˛Ó˚yã˛Ó˚ ˆòáy §yôyÓ˚î Ó›§Ù)ˆÏ Ó˚ xyܲyˆÏÓ˚Ó˚ å§yôyÓ˚îï˛ Ü˛ˆÏÎ˚ܲ ˆ§!Ù Óy ï˛yÓ˚ ˆã˛ˆÏÎ˚G ÓˆÏí˛¸yä ï%˛°lyÎ˚ xyˆÏ°yÓ˚ ï˛Ó˚Aà˜Ïòâ≈ƒ á%Ó z ˆSÈyˆÏê˛y– ~Ùï˛yÓfiÌyÎ˚ ˆï˛yÙÓ˚y ò¢Ù xôƒyˆÏÎ˚ çylˆÏÓ ˆÎñ xyˆÏ°yܲ ï˛Ó˚Aà ~ܲ !Ó®% ˆÌˆÏܲ xlƒ !Ó®%ˆÏï˛ ~ˆÏòÓ˚ §ÇˆÏÎyçܲ §Ó˚°ˆÏÓá˚ y ÓÓ˚yÓÓ˚ àÙl ܲˆÏÓñ˚ ~ Ó˚Ü˛Ù !ÓˆÏÓã˛ly ܲÓ˚y ˆÎˆÏï˛ ˛õyˆÏÓ–˚ ~ z ˛õÌ!ê˛ˆÏܲ xyˆÏ°yܲÓ˚!Ÿ¬ ӈϰ ~ÓÇ ~ zÓ˚)˛õ Ó %§ÇáƒÜ˛ Ó˚!Ÿ¬ ~ܲ!ê˛ xyˆÏ°yܲà%FSÈ ˜ï˛!Ó˚ ܲˆÏÓ˚–  ˛õòyÌ≈!Óòƒy ~ z xôƒyˆÏÎ˚ xyÙÓ˚y xyˆÏ°yÓ˚ Ó˚!Ÿ¬ !ã˛e ÓƒÓ yÓ˚ ܲˆÏÓ˚ xyˆÏ°yÓ˚ ≤Ã!ï˛Ê˛°lñ ≤Ã!ï˛§Ó˚î G !ÓFS%ÈÓ˚ˆÏîÓ˚ âê˛lyà%ˆÏ°yˆÏÜ !ÓˆÏÓã˛ly ܲÓ˚ˆÏÓy– ≤Ã!ï˛Ê˛°l G ≤Ã!ï˛§Ó˚ˆÏîÓ˚ ˆÙÔ!°Ü˛ §)eà%ˆÏ°yˆÏܲ ÓƒÓ yÓ˚ ܲˆÏÓ˚ §Ùï˛° ~ÓÇ ˆày°#Î˚ ≤Ã!ï˛Ê˛°Ü˛ Óy ≤Ã!ï˛§yÓ˚ܲ ï˛° myÓ˚y ≤Ã!ï˛!Ó¡∫ àë˛ˆÏlÓ˚ !Ó£ÏÎ˚!ê˛ xyÙÓ˚y xôƒÎ˚l ܲÓ˚ˆÏÓy– ~Ó˚˛õÓ˚ xyÙÓ˚y Ùyl%ˆÏ£ÏÓ˚ ˆã˛yá § !ܲS%È à%Ó˚%c˛õ)î≈ xyˆÏ°yܲ#Î˚ Îsfy!òÓ˚ àë˛l G ܲyÎ≈l#!ï˛ §¡õˆÏÜ≈˛ Óî≈ly ܲÓ˚ˆÏÓy– xyˆÏ°yÓ˚ ܲ!îܲyÓ˚)˛õ åPARTICLE MODEL OF LIGHTä à!îï˛ñ Ó°!Óòƒy G Ù yܲ£Ï≈ !Ó£ÏÎ˚ܲ !lí˛zê˛ˆÏlÓ˚ ˆÙÔ!°Ü˛ xÓòylà%ˆÏ°yñ xyˆÏ°yÓ˚ ˆ«˛ˆÏe ïÑ˛yÓ˚ ˛õÓ˚#«˛yÙ)°Ü˛ G ï˛y!_¥Ü˛ à˲#Ó˚ xôƒÎ˚là%ˆÏ°y ˆÌˆÏܲ xyÙyˆÏòÓ˚ˆÜÏ ˛ ≤ÃyÎ˚ xrôܲyˆÏÓ˚ ˆÓ˚ˆáÏ ˆÏSÈ– xyˆÏ°yˆÏܲÓ˚ ˛ˆ«˛ˆÏeÏ í˛z!l x@˝Ãl# Ë)˛!Ùܲy ˛õy°l ܲˆÏÓ!˚ SȈ° Ï l– !lí˛zê˛lñ ˆí˛Ü˛yˆÏï˛≈ åDescartesä myÓ˚y ≤ÃhflÏy!Óï˛ xyˆÏ°yÓ˚ ܲ!îܲyÓ˚)ˆÏ˛õÓ˚ xyÓ˚G í˛zߨ!ï˛ §yôl ܲˆÏÓ˚l– ~!ê˛ ôˆÏÓ˚ ˆlGÎ˚y Î˚ ˆÎñ xyˆÏ°yܲ ¢!=˛ ܲï˛Ü˛à%ˆÏ°y «%˛o «%˛o ܲîyÓ˚ §Ùß∫ˆÏÎ˚ â!ê˛ï˛ñ ÎyˆÏòÓ˚ xyˆÏ°yܲ ܲ!îܲy åcorpuscularä ӈϰ– !ï˛!l xyÓ˚G !ÓˆÏÓã˛ly ܲˆÏÓ˚!SȈϰl ˆÎñ xyˆÏ°yÓ˚ ܲ!îܲyà%ˆÏ°y ˲Ó˚ #l !fiÌ!ï˛fiÌy˛õܲ ܲîy– Ó°!ÓòƒyÓ˚ ôyÓ˚îy ˆÌˆÏܲ !ï˛!l ≤Ã!ï˛Ê˛°l G ≤Ã!ï˛§Ó˚ˆÏîÓ˚ ~ܲ!ê˛ §Ó˚° ÙˆÏí˛° ˜ï˛!Ó˚ ܲˆÏÓ˚l– §yôyÓ˚î ˛õÎ≈ˆÏÓ«˛î ˆÌˆÏܲ Ó°y ÎyÎ˚ ˆÎñ ˆÜ˛yˆÏly Ù§,î §Ùï˛° ˆÌˆÏܲ ~ܲ!ê˛ Ó°ÈüÈ~Ó˚ °y!Ê˛ˆÏÎ˚ Gë˛yñ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ §)eà%ˆÏ°y ˆÙˆÏl ã˛ˆÏ°– Îál §Çâ£Ï≈ !fiÌ!ï˛fiÌy˛õܲ Î˚ G ï˛ál ˆÓˆÏàÓ˚ Ùyl ~ܲ z ÌyˆÏܲ– ˆÎˆÏ ï%˛ ï˛°!ê˛ Ù§,îñ ï˛y z ~Ó˚ §Ùyhs˝Ó˚yˆÏ° ˆÜ˛yˆÏly Ó° !ܲÎ˚y ܲˆÏÓ˚ ly– ï˛y z ~ z x!˲Ù%ˆÏá ˲Ó˚ˆÏÓˆÏàÓ˚ í˛z˛õyÇ¢!ê˛ ~ܲ z ÌyˆÏܲ– ≤Ã!ï˛Ê˛°ˆÏl ¢%ô%Ùye ï˛ˆÏ°Ó˚ °¡∫ í˛z˛õyÇ¢!ê˛ xÌ≈yÍ Ë˛Ó˚ˆÏÓˆÏàÓ˚ í˛zÕ‘¡∫ í˛z˛õyÇ¢!ê˛ !Ó˛õÓ˚#ï˛ x!˲Ù%á# Î˚– !lí˛zê˛l x!˲Ùï˛ Óƒ=˛ ܲˆÏÓ˚l ˆÎñ §Ùï˛° ò˛õ≈ˆÏîÓ˚ ÙˆÏï˛y Ù§,î ï˛°à%ˆÏ°y xyˆÏ°yܲ ܲ!îܲyà%ˆÏ°yˆÏܲ ~ܲ z˲yˆÏÓ ≤Ã!ï˛Ê˛!°ï˛ ܲˆÏÓ˚– xyˆÏ°yÓ˚ ≤Ã!ï˛§Ó˚ˆîÏ Ó˚ âê˛ly!ê˛ Óƒyáƒy ܲÓ˚ˆïÏ ˛ !àˆÏÎ˚ !lí˛zê˛l ôˆÏÓ˚ ˆll ˆÎñ ÓyÎ%̊Ó˚ ˆã˛ˆÏÎ˚ ç° xÌÓy ÜÑ˛yˆÏã˛ xyˆÏ°yܲ ܲ!îܲyà%ˆ° Ï yÓ˚ ˆÓà x!ôܲ Î˚– Î!òGñ ˛õÓ˚Ó!ï≈˛ˆÏï˛ xy!Ó‹,Òï˛ Î˚ ˆÎñ ÓyÎ˚%Ó˚ ˆã˛ˆÏÎ˚ çˆÏ° xÌÓy ÜÑ˛yˆÏã˛ xyˆÏ°yÓ˚ o%!ï˛ Ü˛Ù– xyˆÏ°yܲ!ÓK˛yˆÏlñ ˛õÓ˚#«˛y!Óò !lí˛zê˛lñ ï˛y!_¥Ü˛ !lí˛zê˛l xˆÏ˛õ«˛y Ù! Î˚yl– !ï˛!l xˆÏlܲ âê˛ly !lˆÏç z ≤Ãï˛ƒ«˛ ܲˆÏÓ˚!SȈϰlñ ˆÎà%ˆÏ°y xyˆÏ°yÓ˚ ܲ!îܲy ôˆÏÙ≈Ó˚ §y yˆÏ΃ ˆÓyV˛y ܲT˛§yôƒ !SÈ°– í˛zòy Ó˚îfl∫Ó˚)˛õñ çˆÏ°Ó˚ í˛z˛õÓ˚ ˆï˛ˆÏ°Ó˚ ~ܲ!ê˛ ˛õyï˛°y hflψÏÓ˚Ó˚ òÓ˚%l !Ó!˲ߨ ÓˆÏî≈Ó˚ xyˆÏ°y ˆòáy ÎyÎ˚– xyˆÏ°yÓ˚ xyÇ!¢Ü˛ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ ˜Ó!¢T˛ƒG ~Ùl xyÓ˚ ~ܲ!ê˛ í˛zòy Ó˚î– ˆÜ˛í˛z ç°y¢ˆÏÎ˚Ó˚ çˆÏ°Ó˚ !òˆÏܲ ï˛yܲyˆÏ° !lç Ù%ˆÏáÓ˚ ≤Ã!ï˛!Ó¡∫ ˆòáˆÏï˛ ˛õyÎ˚ñ xyÓyÓ˚ §ˆÏAà ç°y¢ˆÏÎ˚Ó˚ ï˛°ˆÏò¢G ˆòáˆÏï˛ ˛õyÎ˚– !lí˛zê˛l x!˲Ùï˛ Óƒ=˛ ܲˆÏÓ˚l ˆÎñ çˆÏ°Ó˚ í˛z˛õÓ˚ xy˛õ!ï˛ï˛ xyˆÏ°yܲ ܲ!îܲyà%ˆÏ°yÓ˚ !ܲS%È ≤Ã!ï˛Ê˛!°ï˛ Î˚ ~ÓÇ !ܲS%È çˆÏ°Ó˚ Ùôƒ !òˆÏÎ˚ §M˛y!°ï˛ Î˚– !ܲv ˆÜ˛yl‰ ˜Ó!¢T˛ƒ xyˆÏ°yܲ ܲ!îܲyà%ˆÏ°yˆÏܲ ò%!ê˛ Ë˛yˆÏà !Ó˲=˛ ܲˆÏÓ˚ˆÏSÈ⁄ !lí˛zê˛lˆÏܲ !ܲS%È x!l!Ÿã˛ï˛ §Ω˛yÓƒ âê˛lyˆÏܲ fl∫#ܲyÓ˚ ܲˆÏÓ˚ !lˆÏï˛ ˆÏÎ˚!SÈ°ñ Îy ˆÜ˛yˆÏly ~ܲ!ê˛ xyˆÏ°yܲ ܲ!îܲy ≤Ã!ï˛Ê˛!°ï˛ ˆÏÓ !ܲ ˆÏÓ lyñ ï˛y !fiÌÓ˚˛ Î˚– Îy ˆ yܲñ xlƒ âê˛lyà%ˆÏ°y Óƒyáƒy ܲÓ˚ˆÏï˛ !àˆÏÎ˚ xyˆÏ°yܲ ܲ!îܲyà%ˆÏ°yÓ˚ xyã˛Ó˚î ~ܲ zÓ˚Ü˛Ù ˆÏÓñ ~Ùl ôˆÏÓ˚ !lˆÏÎ˚!SȈϰl– ~ zÓ˚)˛õ !mã˛y!Ó˚ï˛y xyˆÏ°yÓ˚ ï˛Ó˚Aà ï˛ˆÏ_¥ ˆòáy ÎyÎ˚ ly– ÓyÎ˚% G çˆÏ°Ó˚ !ÓˆÏ˲òï˛ˆÏ° xy˛õ!ï˛ï˛ ï˛Ó˚AàˆÏܲ ò%!ê˛ ò%Ó≈°ï˛Ó˚ ï˛Ó˚ˆÏAà !Ó˲=˛ ܲÓ˚y ˆÎˆÏï˛ ˛õyˆÏÓ˚– 9.2 ˆày°#Î˚ ò˛õ≈î myÓ˚y xyˆÏ°yÓ˚ ≤Ã!ï˛Ê˛°l åREFLECTION OF LIGHT BY SPHERICAL MIRRORSä ≤Ã!ï˛Ê˛°ˆÏlÓ˚ §)eà%ˆÏ°yÓ˚ §! ï˛ xyÙÓ˚y ˛õ!Ó˚!ã˛ï˛– ≤Ã!ï˛Ê˛°l ˆÜ˛yî å≤Ã!ï˛Ê˛!°ï˛ Ó˚!Ÿ¬ G ˛≤Ã!ï˛Ê˛°Ü˛ ï˛° Óy ò˛õ≈ˆÏîÓ˚ í˛z˛õÓ˚ x!˲°ˆÏ¡∫Ó˚ ÙôƒÓï≈˛# ˆÜ˛yîä xy˛õyï˛l ˆÜ˛yî åxy˛õ!ï˛ï˛ Ó˚!Ÿ¬ G x!˲°ˆÏ¡∫Ó˚ ÙôƒÓï≈˛# ˆÜ˛yîä ˛õÓ˚flõÓ˚ §Ùyl Î˚– ~SÈyí˛¸yñ xy˛õ!ï˛ï˛ Ó˚!Ÿ¬ñ ≤Ã!ï˛Ê˛!°ï˛ Ó˚!Ÿ¬ ~ÓÇ xy˛õï˛l !Ó®%ˆÏï˛ ≤Ã!ï˛Ê˛°Ü˛ ï˛ˆÏ°Ó˚ í˛z˛õÓ˚ x!AÜ˛ï˛ x!˲°¡∫ ~ܲ z §Ùï˛ˆÏ° xÓfiÌyl ܲˆÏÓ˚ å!ã˛e 9.1ä– §Ùï˛° Óy Óܲ ˆÎÈüÈˆÜ˛yˆÏly ≤Ã!ï˛Ê˛°Ü˛ 310 ï˛ˆÏ°Ó˚ í˛z˛õÓ˚ ≤Ã!ï˛!ê˛ !Ó®%ˆÏï˛ §)eà%ˆÏ°y ≤ÈÏÎy烖 Î!òG xyÙÓ˚y xyÙyˆÏòÓ˚ xyˆÏ°yã˛ly ܲï˛Ü˛à%ˆÏ°y !ӈϢ£Ï  Ó˚!Ÿ¬ xyˆÏ°yܲ !ÓK˛yl ~ÓÇ xyˆÏ°yܲ#Î˚ Îsfy!ò ÓÜ˛ï˛° xÌ≈yÍ ˆày°#Î˚ ï˛ˆÏ°Ó˚ ˆ«˛ˆÏeÓ˚ §#ÙyÓÂô Ó˚yáˆÏÓy– ~ˆÏ«˛ˆÏe x!˲°¡∫!ê˛ˆÏܲ xy˛õï˛l !Ó®%ˆïÏ ˛ ÓÜ˛ï˛ˆÏ°Ó˚ flõ¢≈ˆÜÏ ˛Ó˚ í˛z˛õÓ˚ °¡∫ ôˆÏÓ˚ ˆlGÎ˚y Î˚– xÌ≈yÍ x!˲°¡∫!ê˛ Óƒy§yô≈ ÓÓ˚yÓÓ˚ Î˚ñ Îy ò˛õ≈ˆÏîÓ˚ Óܲï˛y ˆÜ˛w G xy˛õï˛l !Ó®%Ó˚ §ÇˆÏÎyçܲ §Ó˚°ˆÏÓ˚áy– xyÙÓ˚y zˆÏï˛yÙˆÏôƒ z ˆçˆÏl!SÈ ˆÎñ ˆày°#Î˚ ò˛õ≈ˆÏîÓ˚ çƒy!Ù!ï˛Ü˛ Ùôƒ!Ó®%ˆÏܲ ~Ó˚ ˆÙÓ˚% åpoleä ӈϰ ~ÓÇ ˆày°#Î˚ ˆ°ˆÏ™Ó˚ í˛z=˛ !Ó®%!ê˛ˆÏܲ xyˆÏ°yܲ ˆÜ˛w åoptical centreä ӈϰ– ˆày°#Î˚ ò˛õ≈ˆÏlÓ˚ ˆÙÓ˚% G Óܲï˛y ˆÜ˛ˆÏwÓ˚ §ÇˆÏÎyçܲ ˆÓ˚áyˆÏܲ ≤Ãôyl x«˛ åprincipal axisä ӈϰ– ˆày°#Î˚ ˆ°ˆÏ™Ó˚ ˆ«˛ˆÏe xyˆÏ°yܲ ˆÜ˛w ~ÓÇ Ù%რˆÊ˛yܲyˆÏ§Ó˚ !ã˛e 9.1 ≤Ã!ï˛Ê˛°Ü˛ ï˛ˆÏ°Ó˚ í˛z˛õÓ˚ xy˛õ!ï˛ï˛ Ó˚!Ÿ¬ñ §ÇˆÏÎyçܲ ˆÓ˚áyˆÏܲ ≤Ãôyl x«˛ ӈϰñ Îy ˆï˛yÙÓ˚y ˛õˆÏÓ˚ ˆòáˆÏÓ– ≤Ã!ï˛Ê˛!°ï˛ Ó˚!Ÿ¬ ~ÓÇ x!˲°¡∫!ê˛ ~ܲ z ï˛ˆÏ° xÓfiÌyl ܲˆÏÓ˚– 9.2.1 !ã˛ˆÏ ´Ó˚ Ó˚#!ï˛ åSign conventionä ˆày°#Î˚ ò˛õ≈ˆÏî ≤Ã!ï˛Ê˛°l G ˆày°#Î˚ ˆ°ˆÏ™ ≤Ã!ï˛§Ó˚ˆÏîÓ˚ ≤Ãy§!Aàܲ §)eyÓ!° !lî≈ˆÏÎ˚ñ ò)Ó˚c ˛õ!Ó˚ÙyˆÏ˛õÓ˚ çlƒ xyÙyˆÏòÓ˚ ≤Ã̈ÏÙ xÓ¢ƒ z !ã˛ˆÏ ´Ó˚ Ó˚#!ï˛ @˝Ã î ܲÓ˚ˆÏï˛ ˆÏÓ– ~ z ˛õ%hflψÏܲñ xyÙÓ˚y ÚܲyˆÏï≈˛§#Î˚ !ã˛ ´ Ó˚#!ï˛Û xl%§Ó˚î ܲÓ˚ˆÏÓy– ~ z Ó˚#!ï˛ xl%§yˆÏÓ˚ñ §Ó ò)Ó˚c ò˛õ≈ˆÏîÓ˚ ˆÙÓ%̊ Óy ˆ°ˆÏ™Ó˚ xyˆÏ°yܲ ˆÜ˛w ˆÌˆÏܲ ˛õ!Ó˚Ùy˛õ ܲÓ˚y Î˚– xy˛õ!ï˛ï˛ Ó˚!Ÿ¬Ó˚ x!˲Ù%ˆáÏ ˛õ!Ó˚!Ùï˛ ò)Óc˚ à%ˆ° Ï yˆÏܲ ôlydܲ ~ÓÇ xy˛õ!ï˛ï˛ Ó˚!Ÿ¬Ó˚ !Ó˛õÓ˚#ï˛ x!˲Ù%ˆÏá ˛õ!Ó˚!Ùï˛ ò)Ó˚cà)ˆÏ°yˆÏܲ }îydܲ ôÓ˚y Î˚ å!ã˛e 9.2ä– ò˛õ≈l Óy ˆ°ˆÏ™Ó˚ ≤Ãôyl xˆÏ«˛Ó˚ åx-x«˛ä í˛z˛õÓ˚ °¡∫ ~ÓÇ |ôÁ≈Ùá% # ˛õ!Ó˚!Ùï˛ ˜òâ≈ƒà%ˆ° Ï yˆÏܲ ôlydܲ ôÓ˚y Î˚ å!ã˛e 9.2ä ~ÓÇ !l¡¨Ù%á# ˛õ!Ó˚!Ùï˛ ˜òâ≈ƒà%ˆÏ°yˆÏܲ }îydܲ ôÓ˚y Î˚– §yôyÓ˚î Ó˚#!ï˛ ˆÙˆÏlñ ˆày°#Î˚ ò˛õ≈ˆÏîÓ˚ çlƒ ~ܲ!ê˛ §)e G ˆày°#Î˚ ˆ°ˆÏ™Ó˚ çlƒ ~ܲ!ê˛ §)e !lî≈Î˚ ܲÓ˚y Î˚ñ Îy !Ó!˲ߨ ˆ«˛ˆÏe ≤ÈÏÎ˚yà ܲÓ˚y ˆÎˆÏï˛ ˛õyˆÏÓ˚– 9.2.2 ˆày°#Î˚ ò˛õ≈ˆÏîÓ˚ ˆÊ˛yܲy§ ˜òâ≈ƒ !ã˛e 9.2 ܲyˆÏï≈˛§#Î˚ !ã˛ˆÏ ´Ó˚ Ó˚#!ï˛– åFocal length of spherical mirrorsä ÎáÈl §Ùyhs˝Ó˚y° xyˆÏ°yܲÓ˚!Ÿ¬à%FSÈ (a) ~ܲ!ê˛ xÓï˛° ò˛õ≈î ~ÓÇ (b) ~ܲ!ê˛ í˛z_° ò˛õ≈ˆÏî xy˛õ!ï˛ï˛ Î˚ñ ï˛ál ܲ# âˆÏê˛ ï˛y 9.3 lÇ !ã˛ˆÏe ˆòáyˆÏly ˆÏÎ˚ˆÏSÈ– xyÙÓ˚y ôˆÏÓ˚ ˆl z ˆÎñ Ó˚!Ÿ¬à%ˆÏ°y §Ùy«˛#Î˚ åparaxialä xÌ≈yÍ ~Ó˚y ò˛õ≈ˆÏîÓ˚ ˆÙÓ%̊ PÈüÈ~Ó˚ !lܲê˛Óï≈˛# !Ó®%à%ˆÏ°yˆÏï˛ xy˛õ!ï˛ï˛ Î˚ ~ÓÇ ≤Ãôyl xˆÏ«˛Ó˚ §! ï˛ «%˛o ˆÜ˛yî í˛zͲõߨ ܲˆÏÓ˚– ≤Ã!ï˛Ê˛!°ï˛ Ó˚!Ÿ¬à%ˆÏ°y xÓï˛° ò˛õ≈ˆÏîÓ˚ ≤Ãôyl xˆÏ«˛Ó˚ í˛z˛õ!Ó˚fiÌ F !Ó®%ˆÏï˛ x!˲§yÓ˚# Î˚ [!ã˛e 9.3(a)]– í˛z_° ò˛õ≈ˆÏîÓ˚ ˆ«˛ˆÏe ≤Ã!ï˛Ê˛!°ï˛ Ó˚!Ÿ¬à%ˆÏ°y ≤Ãôyl xˆÏ«˛Ó˚ í˛z˛õ!Ó˚fiÌ F !Ó®% ˆÌˆÏܲ x˛õ§,ï˛ ˆÏFSÈ ÓˆÏ° ÙˆÏl Î˚ [!ã˛e 9.3(b)]– F !Ó®%!ê˛ˆÏܲ ò˛õ≈ˆÏîÓ˚ Ù%რˆÊ˛yܲy§ åPrincipal focusä ӈϰ– Î!ò §Ùy«˛#Î˚ §Ùyhs˝Ó˚y° Ó˚!Ÿ¬à%FS ≤Ãôyl xˆÏ«˛Ó˚ §! ï˛ ˆÜ˛yˆÏly ~ܲ!ê˛ ˆÜ˛yˆÏî xy˛õ!ï˛ï˛ Î˚ñ ï˛ˆÏÓ ≤Ã!ï˛Ê˛!°ï˛ Ó˚!Ÿ¬à%ˆÏ°y ≤Ãôyl xˆÏ«˛Ó˚ í˛z˛õÓ˚ F !Ó®%ˆÏï˛ ~ܲ!ê˛ x!˲°¡∫ ï˛ˆÏ°Ó˚ í˛z˛õÓ˚ ˆÜ˛yˆÏly ~ܲ!ê˛ !Ó®%ˆÏï˛ !Ù!°ï˛ Î˚ åxÓï˛° ò˛õ≈îä Óy !Ó®% ˆÌˆÏܲ x˛õ§,ï˛ ˆÏFSÈ ÓˆÏ° ÙˆÏl Î˚ åí˛z_Ó˚ ò˛õ≈îä– ~ z ï˛°ˆÏܲ ò˛õ≈î!ê˛Ó˚ ˆÊ˛yܲy§ ï˛° åfocal planeä ӈϰ [!ã˛e 9.3(c)]– ˆÜ˛yˆÏly ò˛õ≈ˆÏîÓ˚ ˆÊ˛yܲy§ !Ó®% ~ÓÇ ˆÙÓ˚% PÈüÈ~Ó˚ ÙôƒÓï≈˛# ò)Ó˚cˆÏܲ ò˛õ≈ˆÏîÓ˚ ˆÊ˛yܲy§ ˜òâ≈ƒ ӈϰñ ÎyˆÏܲ 311  ˛õòyÌ≈!Óòƒy !ã˛e 9.3 xÓï˛° G í˛z_° ò˛õ≈ˆÏî ˆÊ˛yܲy§ !Ó®% fmyÓ˚y ≤Ãܲy¢ ܲÓ˚y Î˚– ~ál xyÙÓ˚y ˆòáˆÏÓy ˆÎñ f = R/2, ˆÎáyˆÏl R ò˛õ≈ˆÏîÓ˚ Óܲï˛y Óƒy§yô≈– ~ܲ!ê˛ xy˛õ!ï˛ï˛ Ó˚!Ÿ¬Ó˚ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ çƒy!Ù!ï˛Ü˛ Ó˚)˛õ 9.4È !ã˛ˆÏe ˆòáyˆÏly °– ôˆÏÓ˚y C ° ò˛õ≈ˆÏîÓ˚ Óܲï˛y ˆÜ˛w– ôˆÏÓ˚ lyGñ ≤Ãôyl xˆÏ«˛Ó˚ §Ùyhs˝Ó˚y° ~ܲ!ê˛ Ó˚!Ÿ¬ ò˛õ≈ˆÏîÓ˚ M !Ó®%ˆÏï˛ xy˛õ!ï˛ï˛ ˆÏÎ˚ˆÏSÈ– ï˛ál CM ò˛õ≈ˆÏîÓ˚ í˛z˛õÓ˚ M !Ó®%ˆÏï˛ °¡∫ ˆÏÓ– ôˆÏÓ˚y xy˛õï˛l ˆÜ˛yî θ ~ÓÇ MDñ M !Ó®% ˆÌˆÏܲ ≤Ãôyl xˆÏ«˛Ó˚ í˛z˛õÓ˚ °¡∫– ï˛álñ ∠MCP = θ ~ÓÇ ∠MFP = 2θ ~álñ MD MD tanθ = ~ÓÇ tan 2θ = FD (9.1) CD §Ùy«˛#Î˚ Ó˚!Ÿ¬Ó˚ ˆ«˛ˆÏe θ «%˛o Î˚ ~ÓÇ tanθ ≈ θ, tan 2θ ≈ 2θ– xï˛~Óñ (9.1) §Ù#ܲÓ˚î ˆÌˆÏܲ ˛õy z MD MD =2 FD CD CD Óyñ FD = 2 (9.2) ~álñ θ «%˛o ˆÏ°ñ D !Ó®%ñ P !Ó®%Ó˚ á%Ó Ü˛ySÈyܲy!SÈ ˆÏÓ– xï˛~Óñ FD = f ~ÓÇ !ã˛e 9.4 (a) ˆày°#Î˚ xÓï˛° ò˛õ≈îñ ~ÓÇ CD = R– ï˛ál §Ù#ܲÓ˚î (9.2) ˆÌˆÏܲ ˆ°áy ÎyÎ˚ (b) ˆày°#Î˚ í˛z_° ò˛õ≈ˆÏîÓ˚ ˆ«˛ˆÏe ~ܲ!ê˛ f = R/2 (9.3) xy˛õ!ï˛ï˛ Ó˚!Ÿ¬Ó˚ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ çƒy!Ù!ï˛Ü˛Ó˚)˛õ– 9.2.3 ò˛õ≈ˆÏîÓ˚ §Ù#ܲÓ˚î åThe mirror equationä Î!ò ˆÜ˛yˆÏly !Ó®% ˆÌˆÏܲ !là≈ï˛ Ó˚!Ÿ¬à%ˆÏ°y ≤Ã!ï˛Ê˛°l Óy ≤Ã!ï˛§Ó˚ˆÏîÓ˚ ˛õÓ˚ x˛õÓ˚ ˆÜ˛yˆÏly !Ó®%ˆÏï˛ !Ù!°ï˛ Î˚ñ 312 ï˛ˆÏÓ ˆ§ z !Ó®%!ê˛ˆÏܲ ≤ÃÌÙ !Ó®%Ó˚ ≤Ã!ï˛!Ó¡∫ ӈϰ– Î!ò Ó˚!Ÿ¬à%ˆÏ°y Ó›ï˛ ˆÜ˛yˆÏly !Ó®%ˆÏï˛ x!˲§yÓ˚# Î˚ ï˛ˆÏÓ  Ó˚!Ÿ¬ xyˆÏ°yܲ !ÓK˛yl ~ÓÇ xyˆÏ°yܲ#Î˚ Îsfy!ò ≤Ã!ï˛!Ó¡∫ ˆÏÓ §ò årealäó Î!ò Ó˚!Ÿ¬à%ˆÏ°y !Ù!°ï˛ ly ˆÏÎ˚ ˆÜ˛yˆÏly !Ó®% ˆÌˆÏܲ x˛õ§,ï˛ ˆÏFSÈ ÓˆÏ° ÙˆÏl Î˚ñ ï˛ˆÏÓ ≤Ã!ï˛!Ó¡∫ ˆÏÓ x§ò‰ åvirtualä– Ü˛yˆÏç z ≤Ã!ï˛!Ó¡∫ ° ≤Ã!ï˛Ê˛°l Óy ≤Ã!ï˛§Ó˚î myÓ˚y §,T˛ ˆÜ˛yˆÏly Ó›Ó˚ !Ó®% ˆÌˆÏܲ !Ó®%Ó˚ §ò,¢ï˛y– l#!ï˛àï˛Ë˛yˆÏÓñ ˆÜ˛yˆÏly Ó›Ó˚ ~ܲ!ê˛ !Ó®% ˆÌˆÏܲ !là≈ï˛ ò%!ê˛ Ó˚!Ÿ¬ ˛ṏÏܲ ˆÓ˚áyÇ!Ü˛ï˛ Ü˛ˆÏÓ˚ ~ˆÏòÓ˚ ˆSÈò!Ó®% !lî≈ˆÎÏ Ó˚ ˚ ÙyôƒˆÏÙ z ˆày°#Î˚ ò˛õ≈ˆîÏ ≤Ã!ï˛Ê˛°l myÓ˚y ˆÜ˛yˆÏly !Ó®%Ó˚ ≤Ã!ï˛!Ó¡∫ ˛õyGÎ˚y ÎyÎ˚– Î!òG ÓƒÓ y!Ó˚ܲ ˆ«˛ˆÏe !lˆÏ¡¨Ó˚ Ó˚!Ÿ¬à%ˆÏ°yÓ˚ ÙˆÏôƒ ˆÎÈüÈˆÜ˛yˆÏly ò%!ê˛ˆÏܲ ˆÓˆÏSÈ ˆlGÎ˚y z §%!Óôyçlܲı (i) ˆÜ˛yˆÏly !Ó®% ˆÌˆÏܲ !là≈ï˛ Ó˚!Ÿ¬ Îy ≤Ãôyl xˆÏ«˛Ó˚ §Ùyhs˝Óy˚ °ñ ≤Ã!ï˛Ê˛!°ï˛ Ó˚!Ÿ¬!ê˛ ò˛õ≈ˆÏîÓ˚ ˆÊ˛yܲy§ !òˆÏÎ˚ àÙl ܲˆÏÓ˚– (ii) Ó˚!Ÿ¬!ê˛ xÓï˛° ò˛õ≈ˆÏîÓ˚ Óܲï˛y ˆÜ˛wàyÙ# Óy í˛z_° ò˛õ≈ˆÏîÓ˚ Óܲï˛y !ã˛e 9.5 xÓï˛° ò˛õ≈î myÓ˚y ≤Ã!ï˛!Ó¡∫ àë˛ˆÏlÓ˚ Ó˚!Ÿ¬ !ã˛eÈ– ˆÜ˛w !òˆÏÎ˚ ÎyˆÏFSÈ ÓˆÏ° ÙˆÏl Î˚– ï˛ál ≤Ã!ï˛Ê˛!°ï˛ Ó˚!Ÿ¬!ê˛ ~ܲ z ˛õˆÏÌ ≤Ãï˛ƒyÓï≈˛l ܲˆÏÓ˚– (iii) Ó˚!Ÿ¬!ê˛ xÓï˛° ò˛õ≈ˆÏîÓ˚ ˆÊ˛yܲy§ !òˆÏÎ˚ àÙl ܲˆÏÓ˚ åÓy !Ó®%Ó˚ x!˲Ù%á#ä Óy í˛z_° ò˛õ≈ˆÏîÓ˚ ˆÊ˛yܲy§ !òˆÏÎ˚ àÙl ܲÓ˚ˆÏSÈ ÓˆÏ° åÓy !Ó®%Ó˚ x!˲Ù%á#ä ÙˆÏl Î˚– ≤Ã!ï˛Ê˛!°ï˛ Ó˚!Ÿ¬!ê˛ ≤Ãôyl xˆÏ«˛Ó˚ §Ùyhs˝Ó˚y° Î˚– (iv) Ó˚!Ÿ¬!ê˛ ˆÎÈüÈˆÜ˛yˆÏly ˆÜ˛yˆÏî ˆÙÓ˚%ˆÏï˛ xy˛õ!ï˛ï˛ ˆÏ° ≤Ã!ï˛Ê˛!°ï˛ Ó˚!Ÿ¬!ê˛ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ §)e ˆÙˆÏl ã˛ˆÏ°– 9.5 !ã˛ˆÏe !ï˛l!ê˛ Ó˚!Ÿ¬Ó˚ ˆÓ˚áy!ã˛e ˆòáyˆÏly °– ~áyˆÏl ~ܲ!ê˛ xÓï˛° ò˛õ≈î myÓ˚y AB Ó›Ó˚ A′B′ ≤Ã!ï˛!Ó¡∫ å~ zˆÏ«˛ˆÏeñ §ò‰ä à!ë˛ï˛ Î˚– ~ ܲÌyÓ˚ xÌ≈ ~ z lÎ˚ ˆÎ A !Ó®% ˆÌˆÏܲ ¢%ô%Ùye !ï˛l!ê˛ Ó˚!Ÿ¬ z !là≈ï˛ Î˚– ˆÎÈüÈˆÜ˛yˆÏly í˛zͧ ˆÌˆÏܲ x§#Ù §ÇáƒÜ˛ Ó˚!Ÿ¬ §Ó!òˆÏܲ !là≈ï˛ Î˚– xï˛~Ó A !Ó®% ˆÌˆÏܲ í˛zͲõߨ ≤Ã!ï˛!ê˛ Ó˚!Ÿ¬ xÓï˛° ò˛õ≈ˆÏî ≤Ã!ï˛Ê˛°ˆÏlÓ˚ ˛õÓ˚ A′ !Ó®% !òˆÏÎ˚ àÙl ܲÓ˚ˆÏ° A′ ˆÏÓ A !Ó®%Ó˚ ≤Ã!ï˛!Ó¡∫– ~ál xyÙÓ˚y ò˛õ≈ˆÏîÓ˚ §Ù#ܲÓ˚î xÌ≈yÍ Ó› ò)Ó˚c (u)ñ ≤Ã!ï˛!Ó¡∫ ò)Ó˚c (v) ~ÓÇ ˆÊ˛yܲy§ ˜òˆÏâ≈ƒÓ˚ åf ä ÙˆÏôƒ §¡õܲ≈ fiÌy˛õl ܲÓ˚ˆÏÓy– 9.5 !ã˛e xl%§yˆÏÓ˚ñ A′B′F ~ÓÇ MPF §ÙˆÏܲyî# !eË%˛ç ò%!ê˛ §ò,¢– å§Ùy«˛#Î˚ Ó˚!Ÿ¬Ó˚ çlƒñ MP ˆÜ˛ §Ó˚°ˆÏÓ˚áy ! ˆÏ§ˆÏÓ ôˆÏÓ˚ ˆlGÎ˚y °ñ Îy CPÈüÈ~Ó˚ í˛z˛õÓ˚ °¡∫ä– xï˛~Óñ B′A ′ B′F = PM FP B′A ′ B′F Óy = (äPM = AB) (9.4) BA FP ∠ APB = ∠ A′PB′ GÎ˚yÎ˚ A′B′P ~ÓÇ ABP §ÙˆÏܲyî# !eË%˛çmÎ˚G §ò,¢– xï˛~Óñ B′A ′ B′ P = (9.5) B A BP (9.4) ~ÓÇ (9.5) §Ù#ܲÓ˚îà%ˆÏ°y ï%˛°ly ܲˆÏÓ˚ ˛õy zñ B ′F B ′P − FP B ′P = = (9.6) FP FP BP (9.6) §Ù#ܲÓ˚î!ê˛ ° ò)Ó˚cà%ˆÏ°yÓ˚ ÙˆÏôƒ ~ܲ!ê˛ §¡õÜ≈˛– ~ál xyÙÓ˚y !ã˛ˆÏ ´Ó˚ Ó˚#!ï˛ ≤ÈÏÎ˚yà ܲÓ˚ˆÏÓy– ÙˆÏl Ó˚yáˆÏï˛ ˆÏÓ ˆÎñ Ó› ˆÌˆÏܲ !là≈ï˛ xyˆÏ°y MPN ò˛õ≈î!ê˛Ó˚ !òˆÏܲ ÎyˆÏFSÈ– ~çlƒ ~!ê˛ˆÏܲ ôlydܲ !òܲ ôˆÏÓ˚ ˆlGÎ˚y Î˚– ˆÙÓ˚% P ˆÌˆÏܲ Ó› AB, ≤Ã!ï˛!Ó¡∫ A′B′ G ˆÊ˛yܲy§ FÈüÈ~ ˆ˛õÑÔSÈyˆÏï˛ xyÙyˆÏòÓ˚ xy˛õ!ï˛ï˛ Ó˚!Ÿ¬Ó˚ !Ó˛õÓ˚#ï˛ !òˆÏܲ ˆÎˆÏï˛ Î˚– xï˛~Ó !ï˛l!ê˛ z }îydܲ !ã˛ ´Î%=˛ ˆÏÓ– xï˛~Óñ B′ P = –v, FP = –f, BP = –u 313  ˛õòyÌ≈!Óòƒy (9.6) §Ù#ܲÓ˚ˆÏî Ùylà%ˆÏ°y Ó!§ˆÏÎ˚ ˛õy zñ –v + f –v = –f −u v– f v Óyñ = f u v v = 1+ f u v !òˆÏÎ˚ ˲yà ܲˆÏÓ˚ ˛õy zñ 1 1 1 + = v u f (9.7) ~ z §¡õÜ≈˛!ê˛ ò˛õ≈ˆÏîÓ˚ §Ù#ܲÓ˚î lyˆÏÙ ˛õ!Ó˚!ã˛ï˛– Ó›Ó˚ xyܲyˆÏÓ˚Ó˚ ï%˛°lyÎ˚ ≤Ã!ï˛!ӈϡ∫Ó˚ xyܲyˆÏÓ˚Ó˚ ï%˛°lyˆÏܲ ~ܲ!ê˛ à%Ó˚%c˛õ)î≈ Ó˚y!¢ ! ˆÏ§ˆÏÓ !ÓˆÏÓã˛ly ܲÓ˚y Î˚– ˜Ó˚!áܲ !ÓÓô≈l (m)üÈˆÜ˛ xyÙÓ˚y ≤Ã!ï˛!Ó¡∫ í˛zFã˛ï˛y (h′) ~ÓÇ Ó› í˛zFã˛ï˛y (h)ÈüÈ~Ó˚ xl%˛õyˆÏï˛Ó˚ myÓ˚y §ÇK˛y!Î˚ï˛ Ü˛!Ó˚ ı h′ m= (9.8) h h ~ÓÇ h′ ˆÜ˛ à, #ï˛ !ã˛ˆÏ ´Ó˚ Ó˚#!ï˛ xl%§yˆÏÓ˚ ôlydܲ Óy }îydܲ ôÓ˚y ˆÏÓ– A′B′P ~ÓÇ ABP !eË%˛ç ˆÌˆÏܲ xyÙÓ˚y ˛õy zñ B′A ′ B′P = BA BP – h′ –v !ã˛ˆÏ ´Ó˚ Ó˚#!ï˛ xl%§yˆÏÓ˚ ~!ê˛ ˆÏÓñ h = −u §%ï˛Ó˚yÇñ h′ v m= = – (9.9) h u ~ˆÏ«˛ˆÏe xyÙÓ˚y xÓï˛° ò˛õ≈î myÓ˚y §ò‰ G xÓ¢#£Ï≈ ≤Ã!ï˛!Ó¡∫ àë˛ˆÏlÓ˚ ˆ«˛ˆÏe ò˛õ≈ˆÏîÓ˚ §Ù#ܲÓ˚î (9.7) ~ÓÇ !ÓÓô≈l §)e (9.9) ≤Ã!ï˛¤˛y ܲˆÏÓ˚!SÈ– !ã˛ˆÏ ´Ó˚ Ó˚#!ï˛ ÎÌyÎÌ ≤ÈÏÎ˚yà ܲˆÏÓ˚ ˆòáy ÎyÎ˚ñ ≤Ã!ï˛!Ó¡∫ §ò‰ Óy x§ò‰ Îy z ˆ yܲ ly ˆÜ˛l ˆÎÈüÈˆÜ˛yˆÏly ˆày°#Î˚ ò˛õ≈ˆÏî åxÓï˛° Óy í˛z_°ä ≤Ã!ï˛Ê˛°ˆÏlÓ˚ ≤Ã!ï˛!ê˛ ˆ«˛ˆÏe ~ z §)eà%ˆÏ°y ≤ÈÏÎy烖 9.6 !ã˛ˆÏe ~ܲ!ê˛ xÓï˛° G ~ܲ!ê˛ í˛z_° ò˛õ≈ˆÏîÓ˚ myÓ˚y x§ò‰ ≤Ã!ï˛!ӈϡ∫Ó˚ àë˛l Ó˚!Ÿ¬ !ã˛ˆÏeÓ˚ §y yˆÏ΃ ˆòáyˆÏly ˆÏÎ˚ˆÏSÈ– ˆï˛yÙyˆÏòÓ˚ Îyã˛y z ܲÓ˚ˆÏï˛ ˆÏÓ ˆÎñ ~§Ü˛° ˆ«˛ˆÏeG (9.7) ~ÓÇ (9.9) §Ù#ܲÓ˚îà%ˆÏ°y ≤ÈÏÎyçƒ Î˚ !ܲly– !ã˛e 9.6 (a) Ó›ˆÏܲ ~ܲ!ê˛ xÓï˛° ò˛õ≈ˆÏîÓ˚ P ~ÓÇ FÈüÈ~Ó˚ ÙôƒÓï≈˛# xÓfiÌyˆÏl ˆÓ˚ˆÏáñ ~ÓÇ 314 (b) ~ܲ!ê˛ í˛z_° ò˛õ≈î myÓ˚y ≤Ã!ï˛!Ó¡∫ àë˛l–  Ó˚!Ÿ¬ xyˆÏ°yܲ !ÓK˛yl ~ÓÇ xyˆÏ°yܲ#Î˚ Îsfy!ò í˛zòy Ó˚î 9.1 9.5 !ã˛ˆÏe ~ܲ!ê˛ xÓï˛° ò˛õ≈ˆîÏ Ó˚ ≤Ã!ï˛Ê˛°Ü˛ ï˛°!ê˛Ó˚ l#ˆÏã˛Ó˚ xô≈yÇ¢ xfl∫FSÈ å≤Ã!ï˛Ê˛°l Î˚ lyä ˛õòyÌ≈ myÓ˚y xyÓ,ï˛ Ó˚ˆÏÎ˚ˆÏSÈ– ò˛õ≈î!ê˛Ó˚ §¡ø%ˆÏá Ó˚yáy ~ܲ!ê˛ Ó›Ó˚ ≤Ã!ï˛!ӈϡ∫Ó˚ í˛z˛õÓ˚ ܲ# ≤Ã˲yÓ ˛õí˛¸ˆÏÓ⁄ §Ùyôyl ï%˛!Ù Î˚ˆÏï˛y Óy ˲yÓˆÏÓ ˆÎñ ~ zˆÏ«˛ˆÏe Ó›Ó˚ ˆÜ˛Ó°Ùye xˆÏô≈ܲ ≤Ã!ï˛!Ó¡∫ z ˆòáy ÎyˆÏÓñ í˛zòy Ó˚î 9.1 !ܲv ≤Ã!ï˛Ê˛°ˆÏlÓ˚ §)eyÓ!° ò˛õ≈ˆÏîÓ˚ xÓ!¢T˛ xLjϢÓ˚ ≤Ã!ï˛!ê˛ !Ó®%Ó˚ ˆ«˛ˆÏe z §ï˛ƒ GÎ˚yˆÏï˛ñ §¡õ)î≈ Ó›Ó˚ z ≤Ã!ï˛!Ó¡∫ à!ë˛ï˛ ˆÏÓ– Îy ˆ yܲñ ≤Ã!ï˛Ê˛°Ü˛ ï˛ˆÏ°Ó˚ ˆ«˛eÊ˛° ܲˆÏÙ ÎyGÎ˚yˆÏï˛ ≤Ã!ï˛!ӈϡ∫Ó˚ ≤ÃyÓ°ƒ ܲˆÏÙ ÎyˆÏÓ å~ˆÏ«˛ˆÏeñ xˆÏô≈Ü˛ä– í˛zòy Ó˚î 9.2 9.7 !ã˛e xl%ÎyÎ˚# ~ܲ!ê˛ ˆÙyÓy z° ˆÊ˛ylˆÏܲ ~ܲ!ê˛ xÓï˛° ò˛õ≈ˆÏîÓ˚ ≤Ãôyl x«˛ ÓÓ˚yÓÓ˚ Ó˚yáy ˆÏÎ˚ˆÏSÈ– í˛z˛õÎ%=˛ !ã˛eyAܲˆÏlÓ˚ ÙyôƒˆÏÙ ~Ó˚ ≤Ã!ï˛!Ó¡∫ àë˛l ˆòáyG– !ÓÓô≈l!ê˛ ˆÜ˛l §%£ÏÙ ˆÏÓ lyñ ï˛y Óƒyáƒy ܲˆÏÓ˚y– ò˛õ≈î!ê˛Ó˚ §yˆÏ˛õˆÏ«˛ ˆÊ˛yˆÏlÓ˚ xÓfiÌyˆÏlÓ˚ í˛z˛õÓ˚ ≤Ã!ï˛!ӈϡ∫Ó˚ !ÓÜ,˛!ï˛ !lË≈˛Ó˚ ܲÓ˚ˆÏÓ Ü˛#⁄ !ã˛e 9.7 §Ùyôyl í˛zòy Ó˚î 9.2 9.7 !ã˛ˆÏe ˆÊ˛yl!ê˛Ó˚ ≤Ã!ï˛!Ó¡∫ àë˛ˆÏlÓ˚ Ó˚!Ÿ¬!ã˛e ˆòáyˆÏly ˆÏÎ˚ˆÏSÈ– ≤Ãôyl xˆÏ«˛Ó˚ í˛z˛õÓ˚ °¡∫ ï˛°!ê˛ˆÏï˛ Ó› G ~Ó˚ ≤Ã!ï˛!Ó¡∫!ê˛ §Ùï˛°#Î˚ Î˚ ~ÓÇ ~ˆÏ«˛ˆÏe ≤Ã!ï˛!Ó¡∫!ê˛ §Ù xyÜ,˛!ï˛Ó˚ ˆÏÓñ xÌ≈yÍ B′C = BC– ≤Ã!ï˛!Ó¡∫!ê˛ ˆÜ˛l !ÓÜ,˛ï˛ °ñ ï˛y ï%˛!Ù !lˆÏç ˆÌˆÏܲ z xl%Ë˛Ó Ü˛Ó˚yÓ˚ ˆã˛T˛y ܲˆÏÓ˚y– í˛zòy Ó˚î 9.3 15 cm Óܲï˛y Óƒy§yˆÏô≈Ó˚ ~ܲ!ê˛ xÓï˛° ò˛õ≈ˆÏîÓ˚ §yÙˆÏl ÎÌyܲˆÏÙ (i) 10 cm, (ii) 5 cm ò)Ó˚ˆÏc ~ܲ!ê˛ Ó› Ó§yˆÏly °– ≤Ã!ï˛ˆÏ«˛ˆÏe ≤Ã!ï˛!ӈϡ∫Ó˚ xÓfiÌylñ ≤ÃÜ,˛!ï˛ ~ÓÇ !ÓÓô≈l !lî≈Î˚ ܲˆÏÓ˚y– §Ùyôyl ˆÊ˛yܲy§ ˜òâ≈ƒ f = –15/2 cm = –7.5 cm (i) Ó› ò)Ó˚c u = –10 cm– (9.7) §Ù#ܲÓ˚î xl%§yˆÏÓ˚ñ 1 1 1 + = v – 10 – 7.5 10 × 7.5 Óyñ v= −2.5 = – 30 cm í˛zòy Ó˚î 9.3 ≤Ã!ï˛!Ó¡∫!ê˛ Ó›Ó˚ ~ܲ z ˛õyˆÏ¢ ò˛õ≈î ˆÌˆÏܲ 30 cm ò)ˆÏÓ˚ à!ë˛ï˛ Î˚– v ( −30) ~SÈyí˛¸yñ !ÓÓô≈l m = – =– =–3 u ( −10) ≤Ã!ï˛!Ó¡∫!ê˛ !ÓÓ!ô≈ï˛ñ §ò ~ÓÇ xÓ¢#£Ï≈– 315  ˛õòyÌ≈!Óòƒy (ii) Ó› ò)Ó˚c u = –5 cm– (9.7) §Ù#ܲÓ˚î xl%§yˆÏÓ˚ñ 1 1 1 + = v −5 −7.5 5 × 7.5 Óyñ v= = 15 cm (7.5 5) í˛zòy Ó˚î 9.3 ≤Ã!ï˛!Ó¡∫!ê˛ ò˛õ≈ˆÏîÓ˚ ˆ˛õSȈÏl 15 cm ò)ˆÏÓ˚ à!ë˛ï˛ Î˚– ~!ê˛ x§ò‰ ≤Ã!ï˛!Ó¡∫– v 15 !ÓÓô≈l m = – =– =3 u ( −5) ≤Ã!ï˛!Ó¡∫!ê˛ !ÓÓ!ô≈ï˛ñ x§ò‰ ~ÓÇ §Ù¢#£Ï≈– í˛zòy Ó˚î 9.4 ~ܲ!ê˛ ˛õyÜ≈˛ ܲÓ˚y åparkedä ày!í˛¸ˆÏï˛ ÓˆÏ§ Ìyܲy xÓfiÌyÎ˚ñ R = 2 m Óܲï˛y Óƒy§yˆÏô≈Ó˚ ˛õŸã˛yÍò¢≈# årear viewä ò˛õ≈ˆÏîÓ˚ ÙyôƒˆÏÙ ï%˛!Ù ˆòáˆÏï˛ ˆ˛õˆÏ° ˆÎñ ~ܲçl çàyÓ˚ åJoggerä ˆï˛yÙyÓ˚ !òˆÏܲ ~!àˆÏÎ˚ xy§ˆÏSÈ– Î!ò í˛z=˛ çàyÓ˚ 5 m s–1 o%!ï˛ˆÏï˛ ˆòÑÔí˛¸yˆÏï˛ ÌyˆÏܲñ çàyˆÏÓ˚Ó˚ ≤Ã!ï˛!Ó¡∫ Ü˛ï˛ o%!ï˛ˆÏï˛ x@˝Ã§Ó˚ ˆÏFSÈ ÓˆÏ° ÙˆÏl ˆÏÓñ Îál G z çàyÓ˚ ò˛õ≈î ˆÌˆÏܲ (a) 39 m, (b) 29 m, (c) 19 m, ~ÓÇ (d) 9 m ò)ˆÏÓ˚ ÌyˆÏܲ⁄ §Ùyôyl (9.7) §Ù#ܲÓ˚î ˆÌˆÏܲñ xyÙÓ˚y ˛õy z fu v= u− f í˛z_° ò˛õ≈ˆÏîÓ˚ñ R = 2 m, f = 1 m– ( −39) × 1 39 u = –39 m ~Ó˚ çlƒñ v= = m −39 − 1 40 çàyˆÏÓ˚Ó˚ 5 m s–1 o%!ï˛ˆÏï˛ ˆòÑÔí˛¸yÓyÓ˚ ˆ«˛ˆÏe 1 s ˛õÓ˚ ≤Ã!ï˛!ӈϡ∫Ó˚ xÓfiÌyl v åu = –39 + 5 = –34 ~Ó˚ çlƒä Î˚ (34/35 )m– 1 sÈüÈ~ ≤Ã!ï˛!ӈϡ∫ˆÏÓ˚ xÓfiÌyˆÏlÓ˚ §Ó˚î Î˚ 39 34 1365 − 1360 5 1 − = = = m 40 35 1400 1400 280 xï˛~Óñ Îál çàyÓ˚ ò˛õ≈î ˆÌˆÏܲ 39 m ~ÓÇ 34 mÈüÈ~Ó˚ ÙˆÏôƒ ÌyˆÏܲñ ï˛ál ≤Ã!ï˛!ӈϡ∫Ó˚ àí˛¸ o%!ï˛ (1/280) m s–1 – 1 ~ܲ z˲yˆÏÓñ u = –29 m, –19 m ~ÓÇ –9 mÈüÈ~Ó˚ ˆ«˛ˆÏe ˛≤Ã!ï˛!Ó¡∫!ê˛ ÎÌyܲˆÏÙ m s 1, 150 1 1 1 1 60 ms ~ÓÇ 10 m s o%!ï˛ !lˆÏÎ˚ à!ï˛¢#° ˆÏFSÈ ÓˆÏ° ÙˆÏl ˆÏÓ– í˛zòy Ó˚î 9.4 çàyÓ˚ §Ùo%!ï˛ !lˆÏÎ˚ à!ï˛¢#° ˆÏ°Gñ ˆ§ ò˛õ≈î!ê˛Ó˚ Îï˛ Ü˛ySÈyܲy!SÈ ˆÎˆÏï˛ ÌyܲˆÏÓñ ï˛yÓ˚ ≤Ã!ï˛!ӈϡ∫Ó˚ o%!ï˛ Ü˛Ùyl%§yˆÏÓ˚ Óyí˛¸ˆÏï˛ ÌyܲˆÏÓ ÓˆÏ° ÙˆÏl ˆÏÓ– ~ܲ!ê˛ !fiÌÓ˚ ày!í˛¸ Óy ÓyˆÏ§ ӈϧ Ìyܲy ˆÎÈüÈˆÜ˛yˆÏly Óƒ!=˛ ~ z âê˛ly!ê˛ °«˛ ܲÓ˚ˆÏÓ– à!ï˛¢#° ÎylÓy ˆÏlÓ˚ ˆ«˛ˆÏeñ ˆ˛õSȈÏlÓ˚ ÎylÓy l!ê˛ Î!ò §Ùo%!ï˛ !lˆÏÎ˚ x@˝Ã§Ó˚ ˆÏï˛ ÌyˆÏܲñ ï˛ˆÏÓ ~ܲ zÓ˚Ü˛Ù âê˛ly ˆòáy ÎyˆÏÓ– 9.3 ≤Ã!ï˛§Ó˚î åREFRACTIONä Îál ~ܲà%FSÈ xyˆÏ°yܲÓ˚!Ÿ¬ xlƒ ~ܲ!ê˛ fl∫FSÈ ÙyôƒˆÏÙ xy˛õ!ï˛ï˛ Î˚ñ ï˛ál ~Ó˚ ~ܲyÇ¢ ≤Ã!ï˛Ê˛!°ï˛ ˆÏÎ˚ 316 ≤ÃÌÙ ÙyôƒˆÏÙ !Ê˛ˆÏÓ˚ xyˆÏ§ ~ÓÇ xÓ!¢T˛yÇ¢ !mï˛#Î˚ ÙyôƒˆÏÙ ≤ÈÏÓ¢ ܲˆÏÓ˚– ~ܲ!ê˛ xyˆÏ°yܲÓ˚!Ÿ¬ ~ܲà%FSÈ  Ó˚!Ÿ¬ xyˆÏ°yܲ !ÓK˛yl ~ÓÇ xyˆÏ°yܲ#Î˚ Îsfy!ò xyˆÏ°yܲÓ˚!Ÿ¬ˆÏܲ §)!ã˛ï˛ ܲˆÏÓ˚– ò%!ê˛ ÙyôƒˆÏÙÓ˚ !ÓˆÏ˲òï˛ˆÏ° !ï˛Î≈ܲ˲yˆÏÓ xy˛õ!ï˛ï˛ GÎ˚y xyˆÏ°yܲ Ó˚!Ÿ¬ (0°< i < 90°) x!˲Ù%á ˛õ!Ó˚Óï≈˛l ܲˆÏÓ˚ x˛õÓ˚ ÙyôƒÙ!ê˛ˆÏï˛ ≤ÈÏÓ¢ ܲˆÏÓ˚– ~ z âê˛lyˆÏܲ xyˆÏ°yˆÏܲÓ˚ ≤Ã!ï˛§Ó˚î ӈϰ– ˆfl¨° ˛õÓ˚#«˛yÙ)°Ü˛Ë˛yˆÏÓ !l¡¨!°!áï˛ ≤Ã!ï˛§Ó˚ˆÏîÓ˚ §)eà%ˆÏ°y ˆ˛õˆÏÎ!˚ SȈ° Ï lı (i) xy˛õ!ï˛ï˛ Ó˚!Ÿ¬ñ ≤Ã!ï˛§,ï˛ Ó˚!Ÿ¬ ~ÓÇ xy˛õï˛l !Ó®%ˆÏï˛ ò% z ÙyôƒˆÏÙÓ˚ !ÓˆÏ˲òï˛ˆÏ°Ó˚ í˛z˛õÓ˚ x!˲°¡∫ ~ܲ z §Ùï˛ˆÏ° xÓfiÌyl ܲˆÏÓ˚– (ii) xy˛õï˛l ˆÜ˛yˆÏîÓ˚ §y zl G ≤Ã!ï˛§Ó˚î ˆÜ˛yˆÏîÓ˚ §y zˆÏlÓ˚ xl%˛õyï˛ ô%Óܲ Î˚– ÙˆÏl Ó˚yáˆÏï˛ ˆÏÓ ˆÎñ xy˛õ!ï˛ï˛ Ó˚!Ÿ¬ G ≤Ã!ï˛§,ï˛ Ó˚!Ÿ¬ x!˲°ˆÏ¡Ó∫ ˚ §ˆÏAà ÎÌyܲˆÏÙ xy˛õï˛l ˆÜ˛yî G ≤Ã!ï˛§Ó˚î ˆÜ˛yî í˛zͲõߨ ܲˆÏÓ˚– xyÙÓ˚y ˛õy zñ sin i = n 21 (9.10) !ã˛e 9.8 xyˆÏ°yÓ˚ ≤Ã!ï˛§Ó˚î ~ÓÇ ≤Ã!ï˛Ê˛°l sin r ˆÎáyˆÏl n 21 ~ܲ!ê˛ ô%Óܲñ ÎyˆÏܲ ≤ÃÌÙ ÙyôƒˆÏÙÓ˚ §yˆÏ˛õˆÏ«˛ !mï˛#Î˚ ÙyôƒˆÏÙÓ˚ ≤Ã!ï˛§Ó˚yAܲ årefractive indexä ӈϰ– (9.10) §Ù#ܲÓ˚î!ê˛ ≤Ã!ï˛§Ó˚î §¡õ!Ü≈˛ï˛ ˆfl¨ˆÏ°Ó˚ §)e åSnell’s lawä lyˆÏÙ x!ï˛ ˛õ!Ó˚!ã˛ï˛– xyÙÓ˚y °«˛ ܲÓ˚ˆÏÓy ˆÎñ n 21 ÙyôƒÙmˆÏÎ˚Ó˚ ˜Ó!¢T˛ƒÓy # å~ÓÇ xyˆÏ°yˆÏܲÓ˚ ï˛Ó˚Aà˜ÏòˆÏâ≈ƒÓ˚ í˛z˛õÓ˚G !lË≈˛Ó˚ ܲˆÏÓ˚äñ !ܲv xy˛õï˛l ˆÜ˛yˆÏîÓ˚ í˛z˛õÓ˚ !lË≈˛Ó˚ ܲˆÏÓ˚ ly– (9.10) §Ù#ܲÓ˚î xl%§yˆÏÓ˚ n 21 > 1 ˆÏ° r < i ñ xÌ≈yÍ ≤Ã!ï˛§,ï˛ Ó˚!Ÿ¬!ê˛ x!˲°ˆÏ¡∫Ó˚ !òˆÏܲ ˆÓшÏܲ ÎyÎ˚– ~ˆÏ«˛ˆÏe 1 lÇ ÙyôƒˆÏÙÓ˚ ˆã˛ˆÏÎ˚ 2 lÇ ÙyôƒÙˆÏܲ xyˆÏ°yܲ#Î˚ âlï˛Ó˚ åoptically denserä ÙyôƒÙ Ó°y Î˚ åÓy §ÇˆÏ«˛ˆÏ˛õ âlï˛Ó˚ä– x˛õÓ˚˛õˆÏ«˛ñ n 21 i Î˚ñ xÌ≈yÍ ≤Ã!ï˛§,ï˛ Ó˚!Ÿ¬!ê˛ x!˲°¡∫ ˆÌˆÏܲ ò)ˆÏÓ˚ §ˆÏÓ˚ ÎyÎ˚– ~ˆÏ«˛ˆÏe xy˛õ!ï˛ï˛ Ó˚!Ÿ¬ âlï˛Ó˚ ÙyôƒÙ ˆÌˆÏܲ °â%ï˛Ó˚ ÙyôƒˆÏÙ ≤Ã!ï˛§,ï˛ Î˚– oT˛Óƒ ı xyˆÏ°yܲ#Î˚ âlcˆÏܲ ˲Ó˚ âlˆÏcÓ˚ å~ܲܲ xyÎ˚ï˛ˆÏlÓ˚ ˲Ó˚ä §yˆÏÌ à%!°ˆÏÎ˚ ˆÊ˛°y !ë˛Ü˛ ˆÏÓ ly– ˆÜ˛yˆÏly ~ܲ!ê˛ xyˆÏ°yܲ#Î˚ âl ÙyôƒˆÏÙÓ˚ ˲Ó˚ âlc x˛õÓ˚ ~ܲ!ê˛ xyˆÏ°yܲ#Î˚ °â% ÙyôƒÙ xˆÏ˛õ«˛y ܲÙG ˆÏï˛ ˛õyˆÏÓ˚ åxyˆÏ°yܲ#Î˚ âlc ° ò%!ê˛ ÙyôƒˆÏÙÓ˚ xyˆÏ°yˆÏܲÓ˚ à!ï˛ˆÏÓˆÏàÓ˚ xl%˛õyï˛ä– í˛zòy Ó˚îfl∫Ó˛)˚ õñ ï˛y!˛õ≈l ˆï˛° ~ÓÇ ç°ó ï˛y!˛õ≈l ˆï˛ˆÏ°Ó˚ ˲Ó˚ âlc çˆÏ°Ó˚ ˆã˛ˆÏÎ˚ Ü˛Ù ˆÏ°G ~Ó˚ xyˆÏ°yܲ#Î˚ âlc ˆÓ!¢ Î˚– Î!ò ÙyôƒÙÈüÈ1 ~Ó˚ §yˆÏ˛õˆÏ«˛ ÙyôƒÙÈüÈ2 ~Ó˚ ≤Ã!ï˛§Ó˚yAܲ n 21 ~ÓÇ ÙyôƒÙÈüÈ2 ~Ó˚ §yˆÏ˛õˆÏ«˛ ÙyôƒÙÈüÈ1 ~Ó˚ ≤Ã!ï˛§Ó˚yAܲ n12 Î˚ñ ï˛ˆÏÓ flõT˛ï˛ z 1 n12 = (9.11) n 21 ~ê˛yG ˆòáyˆÏly ÎyÎ˚ ˆÎñ ÙyôƒÙÈüÈ2 ~Ó˚ §yˆÏ˛õˆÏ«˛ ÙyôƒÙÈüÈ3 ~Ó˚ ≤Ã!ï˛§Ó˚yAܲ n 32 Î˚ ï˛ˆÏÓ flõT˛ï˛ z n 32 = n 31 × n 12ñ ˆÎáyˆÏl n 31 ° ÙyôƒÙÈüÈ1 ~Ó˚ §yˆÏ˛õˆÏ«˛ ÙyôƒÙÈüÈ3 ~Ó˚ ≤Ã!ï˛§Ó˚yAܲ– ≤Ã!ï˛§Ó˚ˆÏîÓ˚ §)e ˆÌˆÏܲ !ܲS%È ≤ÃyÌ!Ùܲ Ê˛°yÊ˛° á%Ó § ˆÏç z !ã˛e 9.9 §Ùyhs˝Ó˚y° ˛õyŸª≈Î%=˛ ~ܲ!ê˛ Ê˛°ˆÏܲÓ˚ Ùôƒ !òˆÏÎ˚ ˛õyGÎ˚y ÎyÎ˚– ~ܲ!ê˛ xyÎ˚ï˛yܲyÓ˚ Ê˛°ˆÏܲÓ˚ ò%!ê˛ !ÓˆÏ˲òï˛ˆÏ° ≤Ã!ï˛§,ï˛ Ó˚!Ÿ¬Ó˚ ˛õyŸª≈§Ó˚î– åinterfacesä åÓyÎ%̊ÈüÈܲyã˛ ~ÓÇ Ü˛yã˛ÈüÈÓyÎ%̊ä xyˆÏ°yÓ˚ ≤Ã!ï˛§Ó˚î âˆÏê˛– 9.9 !ã˛e ˆÌˆÏܲ § ˆÏç z ˆòáy ÎyÎ˚ ˆÎñ r2 = i1ñ xÌ≈yÍ !là≈Ùl Ó˚!Ÿ¬ xy˛õ!ï˛ï˛ Ó˚!Ÿ¬Ó˚ §Ùyhs˝Ó˚y° Î˚– 317  ˛õòyÌ≈!Óòƒy ~ˆÏ«˛ˆÏe Ó˚!Ÿ¬Ó˚ ˆÜ˛yˆÏly !Óã%˛ƒ!ï˛ ly âê˛ˆÏ°G xy˛õ!ï˛ï˛ Ó˚!Ÿ¬Ó˚ §yˆÏ˛õˆÏ«˛ !là≈Ù Ó˚!Ÿ¬!ê˛Ó˚ ˛õyŸª≈#Î˚ §Ó˚î âˆÏê˛– xl%Ó˚)˛õ xyÓ˚ ~ܲ!ê˛ ˛õ!Ó˚!ã˛ï˛ ˛õÎ≈ˆÏÓ«˛î °ñ ~ܲ!ê˛ ç°˛õ)î≈ ç°yôyˆÏÓ˚Ó˚ ï˛°ˆÏò¢ !ܲS%Èê˛y í˛z˛õˆÏÓ˚ í˛zˆÏë˛ ~ˆÏ§ˆÏSÈ ÓˆÏ° ÙˆÏl Î˚ å!ã˛e 9.10ä– x!˲°ˆÏ¡∫Ó˚ ܲySÈ ˆÌˆÏܲ ˆòáyÓ˚ ˆ«˛ˆÏe ~ê˛y ˆòáyˆÏly ˆÎˆÏï˛ ˛õyˆÏÓ˚ ˆÎ ≤ÃÜ,˛ï˛ à˲#Ó˚ï˛y åh2ä ˆÜ˛ ÙyôƒˆÏÙÓ˚ åç°ä ≤Ã!ï˛§Ó˚yAܲ !òˆÏÎ˚ ˲yà ܲÓ˚ˆÏ° xy˛õyï˛ à˲#Ó˚ï˛y åh 1ä ˛õyGÎ˚y ÎyÎ˚– ÓyÎ˚%Ù[˛ˆÏ°Ó˚ Ùôƒ !òˆÏÎ˚ xyˆÏ°yÓ˚ ≤Ã!ï˛§Ó˚ˆÏîÓ˚ Ê˛ˆÏ° xˆÏlܲà%ˆÏ°y !ã˛_yܲ£Ï≈ܲ âê˛ly z âˆÏê˛– í˛zòy Ó˚îfl∫Ó˚)˛õñ ÓyÎ˚%Ù[˛ˆÏ°Ó˚ Ùôƒ !òˆÏÎ˚ xyˆÏ°yÓ˚ ≤Ã!ï˛§Ó˚ˆîÏ Ó˚ çlƒ ≤Ãܲ, ï˛ §)ˆÎÏ y≈ òˆÏÎÓ˚ ˚ ˛õ)ˆÓÏ ≈ z ~ÓÇ ≤Ãܲ, ï˛ §)Îy≈ ˆÏhflÓÏ ˚ !ܲS%È ˛õˆÏÓG ˚ §)Î≈ˆÏܲ ˆòáy ÎyÎ˚ å!ã˛e 9.11ä– ≤ÃÜ,˛ï˛ §)ˆÏÎ≈yòÎ˚ Ó°ˆÏï˛ xyÙÓ˚y Ó%!V˛ §)ˆÏÎ≈Ó˚ !òàhs˝ˆÏÓ˚áyˆÏܲ x!ï˛Ü˛Ù ܲÓ˚y– 9.11 !ã˛ˆÏe !òàhs˝ˆÏÓ˚áyÓ˚ §yˆÏ˛õˆÏ«˛ §)ˆÏÎ≈Ó˚ ≤Ãܲ, ï˛ G xy˛õyï˛ xÓfiÌyl ˆòáyˆÏly ˆÏÎ˚ˆÏSÈ– âê˛ly!ê˛ˆÏܲ !ã˛ˆÏe §%flõT˛Ë˛yˆÏÓ ˆòáyˆÏly ˆÏÎ˚ˆÏSÈ– ¢)lƒ ÙyôƒˆÏÙÓ˚ §yˆÏ˛õˆÏ«˛ ÓyÎ%̊Ó˚ ≤Ã!ï˛§Ó˚yAܲ 1.00029– ~ ܲyÓ˚ˆÏî §)ˆÏÎ≈Ó˚ x!˲Ù%ˆÏáÓ˚ xy˛õyï˛ §Ó˚î ≤ÃyÎ˚ (1/2)0 Î˚ ~ÓÇ ~Ó˚ §Ç!Ÿ’T˛ ≤ÃÜ,˛ï˛ §)Î≈yhflÏ G xy˛õyï˛ §)Î≈yˆÏhflÏÓ˚ ÙˆÏôƒ ≤ÃyÎ˚ 2 !Ù!lˆÏê˛Ó˚ ˛õyÌ≈ܲƒ !ã˛e 9.10 (a) x!˲°¡∫˲yˆÏÓ ˆòáyÓ˚ ˆ«˛ˆÏeñ ~ÓÇ Î˚ åí˛zòy Ó˚î 9.5 ˆòˆÏáyä– ~ܲ z ܲyÓ˚ˆÏî §)ˆÏÎ≈yòÎ˚ G §)Î≈yˆÏhflÏÓ˚ §ÙÎ˚ (b) !ï˛Î≈ܲ˲yˆÏÓ ˆòáyÓ˚ ˆ«˛ˆÏe xy˛õyï˛ à˲#Ó˚ï˛y– §)Î≈ˆÏܲ xy˛õyï˛ ò,!T˛ˆÏï˛ !ܲS%Èê˛y ã˛ƒy≤Wzy å!í˛¡∫yܲyÓ˚ä ӈϰ ÙˆÏl Î˚– !ã˛e 9.11 ÓyÎ˚%Ù[˛ˆÏ° ≤Ã!ï˛§Ó˚ˆÏîÓ˚ çlƒ x!@˝ÃÙ §)ˆÏÎ≈yòÎ˚ ~ÓÇ !Ó°!¡∫ï˛ §)Î≈yhflÏ– í˛zòy Ó˚î 9.5 ˛õ,!ÌÓ# !lç xˆÏ«˛Ó˚ §yˆÏ˛õˆÏ«˛ ~ܲÓyÓ˚ â%Ó˚ˆÏï˛ 24 â^˝ê˛y §ÙÎ˚ ˆlÎ˚– ˛õ,!ÌÓ# ˆÌˆÏܲ §)Î≈ˆÏܲ ˆòáˆÏ°ñ §)ˆÏÎ≈Ó˚ 1° §Ó˚ˆÏîÓ˚ çlƒ Ü˛ï˛ §ÙÎ˚ °yàˆÏÓ⁄ í˛zòy Ó˚î 9.5 §Ùyôyl 360° §Ó˚ˆÏîÓ˚ çlƒ §ÙÎ˚ °yˆÏà = 24 â^˝ê˛y– 318 1° §Ó˚ˆÏîÓ˚ çlƒ §ÙÎ˚ °yˆÏà = 24/360 â^˝ê˛y = 4 !Ù!lê˛–  Ó˚!Ÿ¬ xyˆÏ°yܲ !ÓK˛yl ~ÓÇ xyˆÏ°yܲ#Î˚ Îsfy!ò í%˛Óhs˝ !¢¢%ñ ç#ÓlÓ˚«˛# ~ÓÇ ˆfl¨ˆÏ°Ó˚ §)e ~áyˆÏl !ã˛ˆÏe ˛≤Ãò!¢≈ï˛ PQSR ~ܲ!ê˛ xyÎ˚ï˛yܲyÓ˚ §% z!ÙÇ ˛õ%ˆÏ°Ó˚ ܲÌy !ÓˆÏÓã˛ly ܲÓ˚y °– ˛õ%ˆÏ°Ó˚ Óy zˆÏÓ˚ G !Ó®%ˆÏï˛ ÓˆÏ§ Ìyܲy ~ܲçl ç#ÓlÓ˚«˛#ñ §% z!ÙÇ ˛õ%ˆÏ°Ó˚ C !Ó®%ˆÏï˛ í%˛Óhs˝ ~ܲ !¢¢%ˆÏܲ ˆòáˆÏï˛ ˆ˛õ°– Ó˚«˛#!ê˛ ÎÌy§Ω˛Ó l)ƒlï˛Ù §ÙˆÏÎ˚ !¢¢%!ê˛Ó˚ ܲyˆÏSÈ ˆ˛õÑÔSȈÏï˛ ã˛y z°– ôˆÏÓ˚yñ G ~ÓÇ C !Ó®%Ó˚ ÙˆÏôƒ ˛õ%ˆÏ°Ó˚ ôyÓ˚!ê˛ ° SR – ï˛yˆÏܲ G ~ÓÇ C ÈüÈ~Ó˚ §ÇˆÏÎyçܲ §Ó˚°˜ÏÓ!˚ áܲ ˛õÌ GAC !òˆÏÎ˚ xÌÓy GBC ˛õÌ ÓÓ˚yÓÓ˚ñ ˆÎáyˆÏl çˆÏ°Ó˚ ÙˆÏôƒ l)ƒlï˛Ù ˜òˆÏâ≈ƒÓ˚ ˛õÌ!ê˛ ° BC Óy xlƒ ˆÜ˛yˆÏly ˛õÌ GXC !òˆÏÎ˚ ˆÎˆÏï˛ ˆÏÓ– Ó˚«˛#Ó˚ çyly xyˆÏSÈ ˆÎñ Ë)˛!ÙˆÏï˛ ï˛yÓ˚ ˆòÔí˛¸yˆÏlyÓ˚ ˆÓà v1ñ çˆÏ° §Ñyï˛yˆÏÓ˚Ó˚ ˆÓà v2 xˆÏ˛õ«˛y x!ôܲ– ôˆÏÓ˚ lyGñ Ó˚«˛# X !Ó®% !òˆÏÎ˚ çˆÏ° ≤ÈÏÓ¢ ܲÓ˚°– ôˆÏÓ˚yñ GX =l1 ~ÓÇ XC =l 2– xï˛~Óñ G ˆÌˆÏܲ C !Ó®%ˆÏï˛ ˆ˛õÑÔSȈÏï˛ ï˛yÓ˚ §ÙÎ˚ °yàˆÏÓñ l1 l 2 t = + v1 v 2 ~ z §ÙÎ˚!ê˛ l)ƒlï˛Ù ܲÓ˚yÓ˚ çlƒ ~!ê˛ˆÏܲ åXÈüÈfiÌylyLjÏܲÓ˚ §yˆÏ˛õˆÏ«˛ä xÓܲ°l ܲÓ˚ˆÏï˛ ˆÏÓ ~ÓÇ t ÈüÈ~Ó˚ l)ƒlï˛Ù ÙyˆÏlÓ˚ çlƒ X !Ó®%!ê˛ !lî≈Î˚ ܲÓ˚ˆÏï˛ ˆÏÓ– ~ z§Ó Ó#çày!î!ï˛Ü˛ ˛õÂô!ï˛ ˛≤ÈÏÎ˚yà ܲÓ˚yÓ˚ ˛õÓ˚ åÎy ~áyˆÏl ˆòáyˆÏly Î˚!läñ xyÙÓ˚y ˆòáˆÏï˛ ˛õy z ˆÎñ Ó˚«˛#ˆÏܲ ˆ§ z !Ó®% !òˆÏÎ˚ z çˆÏ° ≤ÈÏÓ¢ ܲÓ˚y í˛z!ã˛ï˛ ˆÎáyˆÏl ˆfl¨ˆÏ°Ó˚ §)e!ê˛ !§Âô Î˚– ~!ê˛ ˆÓyV˛yÓ˚ çlƒñ SR Óy %Ó˚ í˛z˛õÓ˚ X !Ó®%ˆÏï˛ LM °¡∫ xÇܲl ܲˆÏÓ˚y– ôˆÏÓ˚yñ ∠GXM = i ~ÓÇ ∠CXL = r– ~ˆÏ«˛ˆÏe ˆòáy ÎyÎ˚ ˆÎñ t l)ƒlï˛Ù ˆÏÓ Îálñ sin i v1 = sin r v 2 xyˆÏ°yÓ˚ ˆ«˛ˆÏe v1/v2 xÌ≈yÍ ¢)lƒ ÙyôƒˆÏÙ xyˆÏ°yÓ˚ à!ï˛ˆÏÓà G xlƒ ˆÜ˛yˆÏly ÙyôƒˆÏÙ xyˆÏ°yÓ˚ à!ï˛ˆÏÓˆÏàÓ˚ xl%˛õyï˛ ° ÙyôƒˆÏÙÓ˚ ≤Ã!ï˛§Ó˚yAܲ n – §ÇˆÏ«˛ˆÏ˛õ Ó°y ÎyÎ˚ñ ï˛Ó˚Aà Óy ܲîy Óy ˛Ùyl%£Ï ˆÎÈüÈˆÜ˛yˆÏly ˆ«˛ˆÏe Îál z ò%!ê˛ ÙyôƒÙ ~ÓÇ ò%!ê˛ ˆÓà §Ç!Ÿ’T˛ ÌyˆÏܲñ ï˛ál ˆÜ˛í˛z Î!ò l)ƒlï˛Ù §ÙÎ˚ !lˆÏï˛ ã˛yÎ˚ñ ï˛yˆÏܲ xÓ¢ƒ z ˆfl¨ˆÏ°Ó˚ §)e xl%§Ó˚î ܲÓ˚ˆÏï˛ ˆÏÓ– 9.4 x˲ƒhs˝ Ó ˚ # î ˛õ) î ≈ ≤Ã!ï˛Ê˛°l å T OTAL I NTERNAL REFLECTIONä Îál xyˆÏ°y xyˆÏ°yܲ#Î˚ âl ÙyôƒÙ ˆÌˆÏܲ xyˆÏ°yܲ#Î˚ °â% ÙyôƒˆÏÙ àÙl ܲˆÏÓñ˚ ï˛ál ò%!ê˛ ÙyôƒˆÏÙÓ˚ !ÓˆÏ˲òï˛ˆÏ° xyˆÏ°y xyÇ!¢Ü˛Ë˛yˆÏÓ ≤ÃÌÙ ÙyôƒˆÏÙ ≤Ã!ï˛Ê˛!°ï˛ Î˚ ~ÓÇ xyÇ!¢Ü˛Ë˛yˆÏÓ !mï˛#Î˚ ÙyôƒˆÏÙ ≤Ã!ï˛§,ï˛ Î˚– ~ z ≤Ã!ï˛Ê˛°lˆÏܲ x˲ƒhs˝Ó˚#î ≤Ã!ï˛Ê˛°l ӈϰ– Îál xyˆÏ°yܲÓ˚!Ÿ¬ âl ÙyôƒÙ ˆÌˆÏܲ °â% ÙyôƒˆÏÙ ≤ÈÏÓ¢ ܲˆÏÓ˚ñ Ó˚!Ÿ¬ ï˛ál ˆÓшÏܲ x!˲°¡∫ ˆÌˆÏܲ ò)ˆÏÓ˚ §ˆÏÓ˚ ÎyÎ˚ñ í˛zòy Ó˚îfl∫Ó˚)˛õñ 9.12 !ã˛ˆÏe Ó˚!Ÿ¬ AO1B– xy˛õ!ï˛ï˛ Ó˚!Ÿ¬ AO1 xyÇ!¢Ü˛ ≤Ã!ï˛Ê˛!°ï˛ åO1Cä ~ÓÇ xyÇ!¢Ü˛ §M˛y!°ï˛ Óy ≤Ã!ï˛§,ï˛ åO1Bä Î˚– ~ zˆÏ«˛ˆÏe ≤Ã!ï˛§Ó˚î ˆÜ˛yî år ä xy˛õï˛l ˆÜ˛yî åi ä xˆÏ˛õ«˛y ÓˆÏí˛¸y Î˚– xy˛õï˛l ˆÜ˛yî Ó,!ÂôÓ˚ §yˆÏÌ §yˆÏÌ ≤Ã!ï˛§Ó˚î ˆÜ˛yîG Ó,!Âô ˛õyÎ˚ñ Îï˛«˛î ˛õÎ≈hs˝ ly AO3 Ó˚!Ÿ¬Ó˚ çlƒ ≤Ã!ï˛§Ó˚î ˆÜ˛yî π/2 ˆÏFSÈ– ï˛ál ≤Ã!ï˛§,ï˛ Ó˚!Ÿ¬!ê˛ ˆÓшÏܲ x!˲°¡∫ ˆÌˆÏܲ ~ˆÏï˛yê˛y z ò)ˆÏÓ˚ §ˆÏÓ˚ ÎyÎ˚ ˆÎñ ï˛y ò% z ÙyôƒˆÏÙÓ˚ !ÓˆÏ˲òï˛° ˆâˆÏ£Ï ÎyÎ˚– 9.12 !ã˛ˆÏe AO3D Ó˚!Ÿ¬ myÓ˚y ~!ê˛ ˆòáyˆÏly ˆÏÎ˚ˆÏSÈ– 319  ˛õòyÌ≈!Óòƒy Î!ò xy˛õï˛l ˆÜ˛yî xyÓ˚G Ó,!Âô ܲÓ˚y Î˚ åˆÎÙl AO4 Ó˚!Ÿ¬äñ ï˛ál ≤Ã!ï˛§Ó˚î §Ω˛Ó Î˚ ly– ~ˆÏ«˛ˆÏe xy˛õ!ï˛ï˛ Ó˚!Ÿ¬ §¡õ)îË≈ ˛yˆÏÓ ≤Ã!ï˛Ê˛!°ï˛ Î˚– ~ âê˛lyˆÏܲ x˲ƒhs˝Ó˚#î ˛õ)î≈ ≤Ã!ï˛Ê˛°l ӈϰ – Îál xyˆÏ°y ˆÜ˛yˆÏly ï˛° ˆÌˆÏܲ ≤Ã!ï˛Ê˛!°ï˛ Î˚ñ §yôyÓ˚îï˛ ~Ó˚ !ܲS%Èê˛y xÇ¢ ≤Ã!ï˛§,ï˛ Î˚– ≤Ã!ï˛Ê˛°Ü˛ ï˛°!ê˛ Îï˛ z Ù§,î ˆ yܲ ly ˆÜ˛lñ ≤Ã!ï˛Ê˛!°ï˛ Ó˚!Ÿ¬Ó˚ ≤ÃyÓ°ƒ §ï˛ï˛ z xy˛õ!ï˛ï˛ Ó˚!Ÿ¬Ó˚ ≤ÃyÓ°ƒ xˆÏ˛õ«˛y Ü˛Ù Î˚– x˛õÓ˚!òˆÏܲñ x˲ƒhs˝Ó#˚ î ˛õ)î≈ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ ˆ«˛ˆÏe xyˆÏ°yÓ˚ ˆÜ˛yˆÏly ≤Ã!ï˛§Ó˚î Î˚ ly– ˆÎ xy˛õï˛l ˆÜ˛yˆÏîÓ˚ çlƒ ≤Ã!ï˛§Ó˚î ˆÜ˛yî 900 Î˚ñ xÌ≈yÍ !ã˛e 9.12 âlÙyôƒˆÏÙ åç°ä ~ܲ!ê˛ !Ó®% A ˆÌˆÏܲñ âl ~ÓÇ °â% ∠AO3Nñ ~ z xy˛õï˛l ˆÜ˛yîˆÏܲ åicä ≤Ãò_ ÙyôƒÙ Î%àˆÏ°Ó˚ ÙyôƒˆÏÙÓ˚ åÓyÎ˚%ä !ÓˆÏ˲òï˛ˆÏ°Ó˚ í˛z˛õÓ˚ !Ó!˲ߨ ˆÜ˛yˆÏî xy˛õï˛ˆÏlÓ˚ çlƒ §ÇÜ˛ê˛ ˆÜ˛yî ӈϰ– ˆfl¨ˆ° Ï Ó˚ §)e å§Ù#ܲÓ˚î 9.10ä ˆÌˆÏܲ xyÙÓ˚y xyˆÏ°yÓ˚ ≤Ã!ï˛§Ó˚î ~ÓÇ x˲ƒhs˝Ó˚#î ≤Ã!ï˛Ê˛°l– ˆòáˆÏï˛ ˛õy z ˆÎñ Î!ò xyˆÏ˛õ!«˛Ü˛ ≤Ã!ï˛§Ó˚yAܲ 1 xˆÏ˛õ«˛y Ü˛Ù Î˚ åˆÎˆÏ ï%˛ sin rÈüÈ~Ó˚ §ˆÏÓ≈yFã˛ Ùyl 1ä ï˛ˆÏÓ sin i ÈüÈ~Ó˚ ~ܲ!ê˛ |ôÁ≈§#Ùy ÌyܲˆÏÓñ ÎyÓ˚ Ê˛ˆÏ° ~ z §)e!ê˛ !§Âô ˆÏï˛ ˛õyˆÏÓ˚ñ xÌ≈yÍ i = ic – ~ˆÏ«˛ˆÏeñ sin ic = n 21 (9.12) ic xˆÏ˛õ«˛y Ó, _Ó˚ iÈüÈ~Ó˚ ÙyˆÏlÓ˚ çˆÏlƒ ˆfl¨ˆÏ°Ó˚ ≤Ã!ï˛§Ó˚ˆÏîÓ˚ §)e!ê˛ áyˆÏê˛ ly ~ÓÇ ï˛y z ˆÏܲyˆÏly ≤Ã!ï˛§Ó˚î §Ω˛Ó Î˚ ly– °â% ÙyôƒÙ 2ÈüÈ~Ó˚ §yˆÏ˛õˆÏ«˛ âl ÙyôƒÙ 1ÈüÈ~Ó˚ ≤Ã!ï˛§Ó˚yAܲñ n12 = 1/sin ic– 9.1 §yÓ˚!îˆÏï˛ !ӈϢ£Ï !ܲS%È §ÇÜ˛ê˛ ˆÜ˛yˆÏîÓ˚ Ùyl !°!˛õÓÂô ܲÓ˚y ° ı §yÓ˚!î 9.1 ÓyÎ˚%Ó˚ §yˆÏ˛õˆÏ«˛ !ܲS%È fl∫FSÈÈ ÙyôƒˆÏÙÓ˚ §ÇÜ˛ê˛ ˆÜ˛yî ÙyôƒˆÏÙÓ˚ í˛z˛õyòyl ≤Ã!ï˛§Ó˚yAܲ §ÇÜ˛ê˛ ˆÜ˛yî ç° 1.33 48.75 ܲyí˛zl ÜÑ˛yã˛ 1.52 41.14 xyˆÏ°yܲ#Î˚ !Êœ˛rê˛ ÜÑ˛yã˛ 1.62 37.31 #Ó˚ܲ 2.42 24.41 x˲ƒhs˝Ó˚#î ˛õ)î≈ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ ~ܲ!ê˛ ≤Ãò¢≈l åA demonstration for total internal reflectionä ~ܲ!ê˛ ˆ°çyÓ˚ ê˛ã≈˛ Óy ˛õˆÏÎ˚rê˛yÓ˚ åÎy xyçܲy° § ç°Ë˛ƒä ÓƒÓ yˆÏÓ˚Ó˚ ÙyôƒˆÏÙ §Ó xyˆÏ°yܲ#Î˚ âê˛ly z x!ï˛ § ˆÏç ≤Ãò¢≈l ܲÓ˚y ˆÎˆÏï˛ ˛õyˆÏÓ˚– ˛õ!Ó˚‹ÒyÓ˚ ç°§ ~ܲ!ê˛ Ü˛yˆÏã˛Ó˚ !ÓܲyÓ˚ lyG– ܲˆÏÎ˚ܲ ˆÊÑ˛yê˛y ò%ô Óy xlƒ ˆÎÈüÈˆÜ˛yˆÏly ≤ð¡∫l çˆÏ° ˆì˛ˆÏ° !òˆÏÎ˚ ~Ùl˲yˆÏÓ xyˆÏ°y!í˛¸ï˛ Ü˛Ó˚y ° ˆÎl ç° !ܲS%Èê˛y ˆây°yˆÏê˛ Î˚– ~ܲ!ê˛ ˆ°çyÓ˚ ˛õˆÏÎ˚rê˛yÓ˚ lyG ~ÓÇ ˆây°yˆÏê˛ çˆÏ°Ó˚ Ùôƒ !òˆÏÎ˚ ~Ó˚ Ó˚!Ÿ¬à%FSȈÏܲ ˛õyë˛yG– ï%˛!Ù ˆòáˆÏÓ ˆÎñ çˆÏ°Ó˚ x˲ƒhs˝Ó˚fiÌ xyˆÏ°yܲ Ó˚!Ÿ¬Ó˚ ˛õÌ!ê˛ ã˛Ü‰˛ã˛ˆÏܲ í˛zIµ°– !ÓܲyˆÏÓ˚Ó˚ ï˛°ˆÏò¢ !òˆÏÎ˚ Ó˚!Ÿ¬à%FSȈÏܲ ~Ùl˲yˆÏÓ ˛õyë˛yG ˆÎl xlƒ≤ÃyˆÏhs˝ çˆÏ°Ó˚ í˛z˛õ!Ó˚ï˛ˆÏ° xy˛õ!ï˛ï˛ Î˚– ~ˆÏ«˛ˆÏeñ Ó˚!Ÿ¬Ó˚ xyÇ!¢Ü˛ ≤Ã!ï˛Ê˛°l åÎyÓ˚ çlƒ l#ˆÏã˛Ó˚ ˆê˛!ӈϰ ~ܲ!ê˛ xyˆÏ°yܲ !Ó®% ˆòáy ÎyˆÏFSÈä ~ÓÇ xyÇ!¢Ü˛ ≤Ã!ï˛§Ó˚î [ ÎyÓ˚ çlƒ ÓyÎ%̊ˆÏï˛ ˆÓ!Ó˚ˆÏÎ˚ xy§y xyˆÏ°yñ SÈyˆÏò ~ܲ!ê˛ xyˆÏ°yܲ !Ó®% ! §yˆÏÓ ˆòáy ÎyˆÏFSÈó 320 !ã˛e 9.13(a)] ˆÏFSÈñ ï˛y ܲ# ï%˛!Ù ˆòáˆÏï˛ ˛õyFSÈ⁄ ~ál !ÓܲyˆÏÓ˚Ó˚ ~ܲ˛õy¢ !òˆÏÎ˚ ˆ°çyÓ˚ Ó˚!Ÿ¬à%ˆÏ°yˆÏܲ  Ó˚!Ÿ¬ xyˆÏ°yܲ !ÓK˛yl ~ÓÇ xyˆÏ°yܲ#Î˚ Îsfy!ò §Ó˚y§!Ó˚ ~Ùl˲yˆÏÓ ˛õyë˛yˆÏï˛ ˆÏÓ ÎyˆÏï˛ çˆÏ°Ó˚ í˛z˛õ!Ó˚ï˛ˆÏ° x!ôܲï˛Ó˚ ï˛#Î≈ܲ˲yˆÏÓ xy˛õ!ï˛ï˛ Î˚ [ !ã˛e 9.13(b)]– ~ál ˆ°çyÓ˚ Ó˚!Ÿ¬à%ˆÏFSÈÓ˚ x!˲Ù%á ~Ùl˲yˆÏÓ ˛õ!Ó˚Óï≈˛l ܲˆÏÓ˚yñ Îï˛«˛î ˛õÎ≈hs˝ ly ï%˛!Ù ~Ùl ~ܲ!ê˛ xy˛õï˛l ˆÜ˛yî ˛õyˆÏFSÈy ÎyÓ˚ çˆÏlƒ ç°ï˛ˆÏ°Ó˚ í˛z˛õˆÏÓ˚ ˆÜ˛yˆÏly ≤Ã!ï˛§Ó˚î Î˚ ly ~ÓÇ Ó˚!Ÿ¬à%FSÈ ˛õ)î≈ ≤Ã!ï˛Ê˛!°ï˛ ˆÏÎ˚ çˆÏ° !Ê˛ˆÏÓ˚ xyˆÏ§– ~!ê˛ z §ÓˆÏã˛ˆÏÎ˚ § ç x˲ƒhs˝Ó˚#î ˛õ)î≈ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ âê˛ly– ~ z ç°ˆÏܲ ~ܲ!ê˛ °¡∫y ˆê˛T˛ !ê˛í˛zˆÏÓ ì˛yˆÏ°y ~ÓÇ 9.13(c)È!ã˛ˆÏeÓ˚ ÙˆÏï˛y í˛z˛õÓ˚ ˆÌˆÏܲ ˆ°çyÓ˚ Ó˚!Ÿ¬à%FSÈ ˛õyë˛yG– ˆ°çyÓ˚ Ó˚!Ÿ¬à%ˆÏFSÈÓ˚ x!˲Ù%á ˛õ!Ó˚Óï≈˛l ܲˆÏÓ˚y ÎyˆÏï˛ ~ܲ!ê˛ !l!ò≈T˛ x!˲Ù%ˆÏáÓ˚ çˆÏlƒ !ê˛í˛zˆÏÓÓ˚ ˆòGÎ˚yˆÏ° xy˛õï˛ˆÏl ≤Ã!ï˛ÓyÓ˚ z Ó˚!Ÿ¬Ó˚ x˲ƒhs˝Ó˚#î ˛õ)î≈ ≤Ã!ï˛Ê˛°l âˆÏê˛– xyˆÏ°yܲ#Î˚ ï˛vˆÏï˛ ˆÎÙlê˛y âˆÏê˛ ~!ê˛ ï˛yÓ˚ xl%Ó˚)˛õ– ܲáˆÏly ˆ°çyÓ˚ Ó˚!Ÿ¬à%FSȈÏܲ §Ó˚y§!Ó˚ ˆòáˆÏÓ ly ~ÓÇ Ü˛yˆÏÓ˚y Ù%ˆÏá ˆÊ˛°ˆÏÓ lyñ ~ z !Ó£ÏÎ˚ ÎbÓyl ÌyܲˆÏÓ– 9.4.1 ≤ÃÜ,˛!ï˛ˆÏï˛ x˲ƒhs˝Ó˚#î ˛õ)î≈ ˛≤Ã!ï˛Ê˛°l ~ÓÇ ï˛yÓ˚ ≤ÃÎ%!=˛àï˛ ≤ÈÏÎ˚yà§Ù) åTotal internal reflection in nature and its technological applicationsä (i) ÙÓ˚#!ã˛Ü˛y åMirageä ı ≤ÃáÓ˚ @˝Ã#ˆÏ‹øÓ˚ !òˆÏlñ í˛z˛õˆÏÓ˚Ó˚ ÓyÎ˚% hflÏÓ˚à%ˆÏ°y xˆÏ˛õ«˛y Ë)˛˛õ,ˆÏ¤˛Ó˚ !lܲê˛Óï≈˛# ÓyÎ˚%hflÏÓ˚à%ˆÏ°y x!ôܲï˛Ó˚ í˛z£÷Ï Î˚– âlˆÏcÓ˚ §yˆÏÌ ÓyÎ˚%Ó˚ ≤Ã!ï˛§Ó˚yAܲ Ó,!Âô ˛õyÎ˚– í˛z£÷Ï ÓyÎ˚% Ü˛Ù âlc Î%=˛ ~ÓÇ z y ¢#ï˛°ï˛Ó˚ ÓyÎ˚% xˆÏ˛õ«˛y Ü˛Ù ≤Ã!ï˛§Ó˚yAܲ !Ó!¢T˛– Î!ò ÓyÎ˚% ≤ÃÓy Ü˛Ù Î˚ñ xÌ≈yÍ ÓyÎ˚% !fiÌÓ˚ ÌyˆÏܲñ ÓyÎ%̊Ó˚ !Ó!˲ߨ hflψÏÓ˚Ó˚ xyˆÏ°yܲ#Î˚ âlc í˛zãï˛ï˛yÓ˚ §yˆÏÌ Ó,!Âô ˛õyÎ˚– Ê˛°fl∫Ó˚)˛õñ àyˆÏSÈÓ˚ ÙˆÏï˛y §%ò#â≈ Ó› ˆÌˆÏܲ xyˆÏ°yñ Ü˛Ù …y§Ùyl ≤Ã!ï˛§Ó˚yÇܲ !Ó!¢T˛ ÓyÎ˚% ÙyôƒˆÏÙÓ˚ Ùôƒ !òˆÏÎ˚ Ë)˛!ÙÓ˚ !òˆÏܲ àÙl ܲˆÏÓ˚– !ã˛e 9.13 ˆ°çyÓ˚ xï˛~Óñ ~ zÓ˚)˛õ ˆÜ˛yˆÏly Ó› ˆÌˆÏܲ xyàï˛ xyˆÏ°yܲÓ˚!Ÿ¬ x!˲°¡∫ ˆÌˆÏܲ ÓyÓ˚ÓyÓ˚ ˆÓшÏܲ ò)ˆÏÓ˚ §Ó˚ˆÏï˛ Ó˚!Ÿ¬à%ˆÏFSÈÓ˚ §y yˆÏ΃ çˆÏ° ÌyˆÏܲ– Î!ò Ë)˛˛õ,ˆ¤Ï ˛Ó˚ !lܲê˛Óï≈˛# ÓyÎ%̊ˆïÏ ˛ xy˛õï˛l ˆÜ˛yî §ÇÜ˛ê˛ ˆÜ˛yî xˆÏ˛õ«˛y ˆÓ!¢ Î˚ñ ï˛ál x˲ƒhs˝Ó#˚ î x˲ƒhs˝Ó˚#î ˛õ)î≈ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ ˛õ)î≈ ≤Ã!ï˛Ê˛°l âˆÏê˛– 9.14(b) !ã˛ˆÏe ~!ê˛ ˆòáyˆÏly °– ò)Ó˚Óï≈˛# ˆÜ˛yˆÏly ò¢≈ˆÏܲÓ˚ !lÜ˛ê˛ ~ z xyˆÏ°y ˛õÎ≈ˆÏÓ«˛î å!ÓܲyˆÏÓ˚Ó˚ ܲyã˛ á%Ó Ë)˛˛õ,ˆÏ¤˛Ó˚ l#ˆÏã˛Ó˚ ˆÜ˛yˆÏly !Ó®% ˆÌˆÏܲ˛ xy§ˆÏSÈ ÓˆÏ° ÙˆÏl ˆÏÓ– fl∫y˲y!Óܲ˲yˆÏÓ z ò¢≈ܲ ÙˆÏl ܲˆÏÓ˚ ˆÎñ ˛õyï˛°y GÎ˚yÓ˚ çlƒ ~Ó˚ ˆÜ˛yˆÏly §%ò#â≈ Ó›Ó˚ !lܲê˛Óï≈˛# ç°y¢ˆÏÎ˚Ó˚ ÙˆÏï˛y Ë)˛!Ù ˆÌˆÏܲ xyˆÏ°y ≤Ã!ï˛Ê˛!°ï˛ ˆÏFSÈ– ò)Ó˚Óï≈˛# fiÌyˆÏl myÓ˚y ≤Ã!ï˛§Ó˚îˆÏܲ x@˝Ãy ƒ Ìyܲy ò#â≈ Ó›Ó˚ ~ zÓ˚)˛õ í˛zˆÏŒê˛y ≤Ã!ï˛!Ó¡∫ ò¢≈ˆÏܲÓ˚ ò,!T˛ºÙ §,!T˛ ܲˆÏÓ˚– ~ z âê˛lyˆÏܲ ÙÓ˚#!ã˛Ü˛y ӈϰ– ܲÓ˚y °ä– !ӈϢ£Ï ܲˆÏÓ˚ í˛z£÷Ï ÙÓ˚%Ë)˛!ÙˆÏï˛ ~ z ôÓ˚ˆÏlÓ˚ ÙÓ˚#!ã˛Ü˛y ~ܲ!ê˛ fl∫y˲y!Óܲ âê˛ly– ˆï˛yÙyˆÏòÓ˚ ˆÜ˛í˛z ˆÜ˛í˛z Î˚ˆÏï˛y °«˛ ܲˆÏÓ˚SÈñ í˛z_Æ @˝Ã#ˆÏ‹øÓ˚ !òˆÏl !˛õˆÏã˛Ó˚ ˜ï˛!Ó˚ !ÓhflÏ#î≈ Ó˚yhflÏyÎ˚ñ !ӈϢ£Ïï˛ çyï˛#Î˚ §í˛¸ˆÏܲñ Óy§ Óy !ã˛e 9.14 (a) Ë)˛˛õ,ˆÏ¤˛Ó˚ í˛z˛õˆÏÓ˚Ó˚ ÓyÎ˚% §Ùí˛z£÷Ïï˛yÎ˚ ÌyܲˆÏ° ˆÜ˛yˆÏly ò¢≈ܲ ~ܲ!ê˛ àySȈÏܲ ~Ó˚ xÓfiÌyˆÏl ˆÎÙl ˆòˆÏáñ (b) Îál Ë)˛˛õ,¤˛ §Ç°@¿ í˛z£÷Ïï˛Ù ÓyÎ˚%hflÏÓ˚à%ˆÏ°yÓ˚ §yˆÏÌ Ë)˛˛õ,ˆÏ¤˛Ó˚ ܲySÈyܲy!SÈ ÓyÎ˚%hflÏÓ˚à%ˆÏ°yÓ˚ í˛z£÷Ïï˛y ˛õ!Ó˚Óï≈˛l¢#°ñ ò)Ó˚Óï≈˛# ˆÜ˛yˆÏly àySÈ ˆÌˆÏܲ xyàï˛ xyˆÏ°yÓ˚ ˛õ)î≈ ≤Ã!ï˛Ê˛°l âê˛ˆÏï˛ ˛õyˆÏÓ˚ ~ÓÇ ˛õÎ≈ˆÏÓ«˛ˆÏܲÓ˚ !lÜ˛ê˛ àySÈ!ê˛Ó˚ 321 xy˛õyï˛ ≤Ã!ï˛!Ó¡∫ñ àySÈ!ê˛ ç°y¢ˆÏÎ˚Ó˚ ܲySÈyܲy!SÈ xyˆÏSÈ ~Ùl ò,!T˛ºˆÏÙÓ˚ §,!T˛ ܲÓ˚ˆÏï˛ ˛õyˆÏÓ˚–  ˛õòyÌ≈!Óòƒy ˆÜ˛yˆÏly ày!í˛¸ˆÏï˛ Ü˛ˆÏÓ˚ ã˛°yÓ˚ §ÙÎ˚ Ó˚yhflÏyˆÏܲ !˲çy ӈϰ ÙˆÏl Î˚– !ܲvñ Îál ï%˛!Ù G z çyÎ˚àyÎ˚ ˆ˛õÑÔSÈyGñ ï˛ál !˲çy Ó˚yhflÏyÓ˚ ˆÜ˛yˆÏly !lò¢≈l ˛õyGÎ˚y ÎyÎ˚ ly– ~ê˛yG ÙÓ˚#!ã˛Ü˛yÓ˚ çˆÏlƒ âê˛ˆÏSÈ– (ii) #Ó˚ܲ åDiamond ä: ã˛Ùܲ≤Ãò ÅIµˆÏ°ƒÓ˚ çlƒ #Ó˚ܲ ˛õ!Ó˚!ã˛ï˛– #Ó˚ˆÏܲÓ˚ !Ë˛ï˛ˆÏÓ˚ xyˆÏ°yÓ˚ x˲ƒhs˝Ó˚#î ˛õ)î≈ ≤Ã!ï˛Ê˛°l z Ù)°ï˛ ~Ó˚ í˛zIµ°ï˛yÓ˚ ܲyÓ˚î– #Ó˚ܲÈüÈÓyÎ˚% !Ó˲ˆÏòï˛ˆÏ° §ÇÜ˛ê˛ ˆÜ˛yî (≅ 24.4°) á%Ó z «%˛o– ï˛y z xyˆÏ°yܲ Îál #Ó˚ˆÏܲ ≤ÈÏÓ¢ ܲˆÏÓ˚ ï˛ál ~Ó˚ !Ë˛ï˛ˆÏÓ˚ x!ôܲyÇ¢ ˆ«˛ˆÏe z xyˆÏ°yÓ˚ x˲ƒhs˝Ó#˚ î ˛õ)î≈ ≤Ã!ï˛Ê˛°l âˆÏê˛– ≤ÃÜ,˛!ï˛ˆÏï˛ ≤ÃyÆ #Ó˚ܲ ܲòy!ã˛ï˛ zÈ È~Ó˚ §Ó≈çl !Ó!òï˛ í˛zI° µ ï˛y ≤Ãò¢≈l ܲˆÏÓ–˚ #Ó˚ܲ ܲyê˛yÓ˚ ܲy!Ó˚àÓ˚ˆòÏ Ó˚ ≤ÃÎ!% =˛àï˛ ò«˛ï˛y z #Ó˚ˆÏܲÓ˚ í˛zIµ° ˆçƒy!ï˛Ó˚ Ù)° ã˛y!Óܲy!벖 #Ó˚ܲ á[˛ˆÏܲ í˛z˛õÎ%=˛Ë˛yˆÏÓ ˆÜ˛ˆÏê˛ ~Ó˚ !Ë˛ï˛ˆÏÓ˚ xyˆÏ°yÓ˚ ˛õ%l/˛õ%l/ x˲ƒhs˝Ó˚#î ˛õ)î≈ ≤Ã!ï˛Ê˛°l âê˛ˆÏly ÎyÎ˚– !ã˛e 9.15 Ó˚!Ÿ¬Ó˚ 90° ~ÓÇ 180° ˆÜ˛yˆÏî !Óã%˛ƒ!ï˛Ó˚ çlƒ xÌÓy (iii) !≤ÃçÙ åPrism ä : xyˆÏ°yÓ˚ 90° Óy 180° !Óã%˛ƒ!ï˛Ó˚ x˛õ!Ó˚Ó!ï≈˛ï˛ xyܲyˆÏÓ˚Ó˚ xÓ¢#£Ï≈ ≤Ã!ï˛!Ó¡∫ ˛õyGÎ˚yÓ˚ çlƒ çlƒ !ӈϢ£Ï˲yˆÏÓ ≤Ã›ï˛ Ü˛Ó˚y ådesignedä !≤ÃçˆÏÙ !ӈϢ£Ï˲yˆÏÓ ≤Ã›ï˛ Ü˛Ó˚y !≤ÃçˆÏÙ xyˆÏ°yÓ˚ x˲ƒhs˝Ó˚#î x˲ƒhs˝Ó#˚ î ˛õ)î≈ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ âê˛ly!ê˛ ÓƒÓ yÓ˚ ܲÓ˚y Î˚ [ !ã˛e ˛õ)î≈ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ âê˛ly!ê˛ ÓƒÓ yÓ˚ ܲÓ˚y Î˚– 9.15(a) ~ÓÇ (b)]– xyܲyÓ˚ x˛õ!Ó˚Ó!ï≈˛ï˛ ˆÓ˚ˆÏá xÓ¢#£Ï≈ ≤Ã!ï˛!Ó¡∫ ˛õyGÎ˚yÓ˚ ˆ«˛ˆÏeG ~ zÓ˚)˛õ !≤ÃçÙ ÓƒÓ yÓ˚ ܲÓ˚y Î˚ [ !ã˛e 9.15(c)]– ≤ÃÌÙ ò%!ê˛ ˆ«˛ˆÏeñ !≤ÃçˆÏÙÓ˚ í˛z˛õyòyˆÏlÓ˚ §ÇÜ˛ê˛ ˆÜ˛yî xÓ¢ƒ z 45° xˆÏ˛õ«˛y Ü˛Ù ˆÏï˛ ˆÏÓ– §yÓ˚!î 9.1 ˆÌˆÏܲ xyÙÓ˚y ˆò!á ˆÎñ ܲyí˛zl ܲyã˛ ~ÓÇ xyˆÏ°yܲ#Î˚ âl !Êœ˛rê˛ Ü˛yã˛ í˛z˲ˆÏÎ˚Ó˚ ˆ«˛ˆÏe z ~!ê˛ §ï˛ƒ– (iv) xyˆÏ°yܲ#Î˚ ï˛v åOptical fibresä : x!í˛G ~ÓÇ !˲!í˛G §ÇˆÏÜ˛ï˛ Ó %ò)Ó˚ ˛õÎ≈hs˝ ˆ≤ÃÓ˚î ܲÓ˚yÓ˚ çlƒ xyçܲy° xyˆÏ°yܲ#Î˚ ï˛v Óƒy˛õܲ˲yˆÏÓ ÓƒÓ ,ï˛ Î˚– xyˆÏ°yܲ#Î˚ ï˛vˆÏï˛G x˲ƒhs˝Ó#˚ î ˛õ)î≈ ≤Ã!ï˛Ê˛°ˆÏlÓ˚ âê˛ly!ê˛ ÓƒÓ yÓ˚ ܲÓ˚y Î˚– í˛zߨï˛ÙyˆÏlÓ˚ !Ó!Ù!◊ï˛ ÜÑ˛yã˛‡ˆÜ˛yÎ˚yç≈ ï˛v myÓ˚y xyˆÏ°yܲ#Î˚ ï˛v ˜ï˛!Ó˚ ܲÓ˚y Î˚– ≤Ã!ï˛!ê˛ ï˛v ~ܲ!ê˛ ÙIy åcoreä ~ÓÇ xyÓÓ˚î åcladdingä !òˆÏÎ˚ à!ë˛ï˛– ÙIyÓ˚ í˛z˛õyòyˆÏlÓ˚ ≤Ã!ï˛§Ó˚yAܲ xyÓÓ