UNIVERSITY OF NAIROBI COLLEGE OF EDUCATION AND EXTERNAL STUDIES

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1 UNIVERSITY OF NAIROBI COLLEGE OF EDUCATION AND EXTERNAL STUDIES COURSE TITLE: BED (SCIENCE) UNIT TITLE: WAVES AND OPTICS UNIT CODE: SPH 103 UNIT AUTHOR: PROF. R.O. GENGA DEPARTMENT OF PHYSICS UNIVERSITY OF NAIROBI LECTURE NOTES

2 UNIT AIM: At the end of this unit you would be able to understand, apply and acknowledge the importance of physical processes involved in waves and optics. UNIT OUTLINE The unit shall be studied under three major topics, that is, wave motion, sound waves and wave geometry (optics), respectively. Details are given below. TOPIC 1: WAVE MOTION 1.1 INTRODUCTION DESCRIPTION OF WAVE MOTION WAVES IN ONE-DIMENSION THE GENERAL EQUATION OF WAVE MOTION ELASTIC (LONGITUDINAL) WAVES IN A SOLID AND IN A STRING Elasticity Elasticity and Plasticity Elastic (Longitudinal) Waves in a Solid Elastic (Longitudinal) Waves in a String TRANSVERSE WAVES IN A STRING Transverse Travelling Waves in a String Transverse Standing Waves in a String Resonance Traveling Elastic Waves in a Bar WAVES IN TWO-DIMENSIONS Wavefronts Reflection of Waves Refraction of Waves Interference of Waves Diffraction of Waves SURFACE WAVES IN A LIQUID WHAT PROPAGATES IN WAVE MOTION? GROUP VELOCITY

3 TOPIC 2: SOUND WAVES 2.1 INTRODUCTION PRESSURE WAVES IN A GAS COLUMN ADIABATIC CHARACTER OF A LONGITUDINAL WAVE WAVES IN THREE-DIMENSIONS Spherical Waves in a Fluid Spherical Harmonic Pressure Waves INTENSITY OF SOUND WAVES Intensity of Sinusoidal Waves along a Rod Intensity of Sinusoidal waves in a gas column Intensity of Spherical Wave Intensity Level and Loudness STANDING LONGITUDINAL ELASTIC WAVES VIBRATING SYSTEMS AND SOURCES OF SOUND Sound from Vibrating String Sound from Vibrating Air Column End-correction of Pipes or Tubes Effects of Temperature and End-correction on Pitch of Pipes or Tubes RESONANCE IN A PIPE OR TUBE Demonstration of Phenomenon of Resonance in Air Column Demonstration of Phenomenon of Acoustic Resonance Applications of Resonance Hazards of Resonance CONSEQUENCES OF REFLECTION OF SOUND CONSEQUENCES OF REFRACTION OF SOUND CONSEQUENCES OF DIFFRACTION OF SOUND CONSEQUENCE OF INTERFERENCE FO SOUND : BEATS APPLICATIONS OF BEATS THE DOPPLER EFFECT APPLICATIONS OF THE DOPPLER EFFECT APPLICATIONS OF SOUND: ULTRASOUND AND MEDICAL IMAGING 140

4 TOPIC 3: WAVE GEOMETRY (OPTICS) 3.1 INTRODUCTION RAYS AND BEAM OF LIGHT FERMAT S PRINCIPLE APPLICATIONS OF FERMAT S PRINCIPLE REFRACTIVE INDEX THE PRINCIPLE OF REVERSIBILITY OF LIGHT CONSEQUENCES (EFFECTS) OF REFRACTION REAL AND APPARENT DEPTH Expression of Refractive Index in terms of Real and Apparent Depth Expression of Object distant d in terms of Medium Thickness t and refractive index n TOTAL INTERNAL REFLECTION AND CRITICAL ANGLE CONSEQUENCE OF TOTAL INTENAL REFLECTION RELATION BETWEEN CRITICAL ANGLE AND REFRACTIVE INDEX APPLICATIONS OF TOTAL INTERNAL REFLECTION APLANATIC POINTS AND APLANATIC SURFACES Aplanatic Points and Aplanatic Surface for Reflection Aplanatic Points and Aplanatic Surface for Refraction Conjugate Points and Conjugate planes APPLICATION OF APLANATIC POINTS OF A SPHERICAL SURFACE REFLECTION AT A SPHERICAL SURFACE OF SMALL APERTURE Spherical Surfaces (Mirrors) Reflection of Narrow Parallel Beam from Spherical Surfaces BASIC DEFINITIONS Relation between the Focal Length of a Spherical Surface and its Radius of Curvature Sign Conventions CONSTRUCTION OF RAY DIAGRAMS IMAGES FORMED BY A CONCAVE SPHERICAL SURFACE IMAGES FORMED BY A CONVEX SPHERICAL SURFACE MAGNIFICATION FORMULA.179

5 3.21 DESCARTES FORMULA FOR REFLECTION AT A SPHERICAL SURFACE OF SMALL APERTURE Focal Point REFLECTION AT A SPHERICAL SURFACE OF LARGE APERTURE SPHERICAL SURFACE ABERRATIONS Spherical Aberration Marginal (Outer Zone) Rays Parallel to the Axis of Spherical Surfaces cross the Axis inside the Focal Point F Methods of Minimizing Spherical Aberration Astigmatism Astigmatism in Eye Methods of Minimizing Astigmatism APPLICATIONS OF REFLECTING SPHERICAL SURFACES REFRACTION AT A SPHERICAL SURFACE OF SMALL APERTURE Descartes Formula for Refraction at a Spherical Surface of Small Aperture Focal Points REFRACTION AT A SPHERICAL SURFACE OF LARGE APERTURE SPHERICAL ABERRATION OF A SPHERICAL REFRACTING SURFACE LENSES Types of Lenses Power of Lens THE THIN LENS Ray Tracing BASIC DEFINITIONS CONSTRUCTION OF RAY DIAGRAMS FORMATION OF IMAGES BY A CONVERGING LENS FORMATION OF IMAGES BY A DIVERGING LENS MAGNIFICATION DESCARTES FORMULA FOR A THIN LENS Focal Points DESCARTES FORMULAR FOR A COMBINATION OF TWO LENSES WITH POSITIONS OF THEIR FOCI SEPARATED BY DISTANCE t.222

6 3.37 FOCAL LENGTH OF TWO THIN LENSES IN CONTACT THE LARGE LENS LENS ABERRATIONS Introduction Spherical Aberration Effects of Lens Shape on Spherical Aberration Methods of Minimizing Spherical Aberration Coma Radius of Comatic Circle Effects of Lens Shape and Position, on Coma Coma and the Sine Condition Practical Elimination of Coma from Optical Systems Astigmatism Astigmatism in Eye Curvature of the Field Methods of Minimizing Curvature of the Field Distortion Barrel Distortion Pin-cushion Distortion Chromatic Aberration Methods of Minimizing Chromatic Aberration THE PRISM Refraction Through Prism OPTICAL INSTRUMENTS The Simple Microscope The Compound Microscope The Telescope The Projector SOLUTIONS TO SELF ASSESSMENT QUESTIONS WAVE MOTION SOUND WAVES WAVE GEOMETRY (OPTICS).290

7 REFERENCES You may read the following textbooks to assist you understand lecture notes whenever it is necessary. 1. University Optics. Vol. 1; by D.W. Tenquist, R.M. Whittle and J. Yarwood; Published by London Ilife Books Ltd. (1969). 2. Fundamentals of Optics, Third Edition; by F.A. Jenkins and H.E. White; Published by McGraw-Hill Kogakusha, Ltd. 3. Physics, Second Edition Expanded; by H.C. Ohanian; Published by W.W. Norton and Company. (1989) 4. Physics; by C. Zafiratos; Published by John Wiley & Sons, Inc.(1975) 5. University Physics, 5 th edition; by F.W. Sears, M.W. Zamansky and H.D. Young; Published by Addison-Wesley Publishing Company. (1978).

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