TEXT-BOOK OF PHYSICS
CHAPTER 1 INTERFERENCE CHAPTER 2 DIFFRACTION 23 CHAPTER 3 POLARIZATION 45 CHAPTER 4 CRYSTAL STRUCTURES 63 CHAPTER 5 X RAY DIFFRACTION 81 CHAPTER 6 LASERS 115 CHAPTER 7 FIBRE OPTICS 141 CHAPTER 8 NON DESTRUCTIVE TESTING USING 167 CONTENTS INTERFERENCE 1 1 INTRODUCTION WHEN A NUMBER OF WAVES PASS THROUGH A POINT IN A MEDIUM AT THE SAME TIME THEY COMBINE TO PRODUCE A RESULTANT WAVE HAVING DI ERENT AMPLITUDE AND HENCE INTENSITY THAN THE INDIVIDUAL WAVES AT THAT POINT TH IS PROCESS IS KNOWN AS THE INTERFERENCE TH E RESULTANT INTENSITY AT A POINT IS DUE TO THE COMBINED IN UENCE OF ALL THE WAVES THAT PASS THROUGH THE POINT INTERFERENCE PRODUCES MODI CATION IN THE DISTRIBUTION OF INTENSITY OF LIGHT INTERFERENCE HAVE BEEN OBSERVED WITH LIGHT WAVES SOUND WAVES WATER WAVES ETC INTERFERENCE CAN BE EXPLAINED USING THE PRINCIPLE OF SUPERPOSITION OF WAVES 1 2 SUPERPOSITION OF WAVES TH E PRINCIPLE OF SUPERPOSITION OF WAVES STATES THAT THE RESULTANT DISPLACEMENT AT A POINT IN A MEDIUM IS THE ALGEBRAIC SUM OF THE DISPLACEMENTS DUE TO INDIVIDUAL WAVES PASSING THROUGH THAT POINT SIMULTANEOUSLY SUPERPOSITION TAKES PLACE WHEN TWO OR MORE WAVES PASS THROUGH A POINT IN A MEDIUM TO UNDERSTAND SUPERPOSITION WE CONSIDER TWO WAVES PASSING THROUGH A POINT IN A MEDIUM LET Y1 BE THE DISPLACEMENT OF A PARTICLE AT THAT POINT DUE TO THE RST WAVE IN THE ABSENCE OF SECOND WAVE AND Y2 BE THE DISPLACEMENT AT THAT POINT DUE TO THE SECOND WAVE IN THE ABSENCE OF THE RST WAVE TH E RESULTANT DISPLACEMENT R AT THAT POINT WHEN BOTH THE WAVES ACT SIMULTANEOUSLY IS R Y1 Y2 TH E SIGN IS USED WHEN BOTH DISPLACEMENTS ARE IN THE SAME DIRECTION AND THE SIGN IS USED WHEN THE TWO DISPLACEMENTS ARE IN OPPOSITE DIRECTIONS C H A P T E R 1 1 1 3 YOUNG S DOUBLE SLIT EXPERIMENT IN 1801 TH OMAS YOUNG RST DEMONSTRATED INTERFERENCE OF LIGHT HIS EXPERIMENTAL SET UP IS SHOWN IN FIG 1 1 AS SHOWN IN FIG 1 1 HE PASSED SUN LIGHT THROUGH A NARROW PIN HOLE S ON AN OPAQUE SURFACE AND THEN THROUGH TWO CLOSELY SPACED PIN HOLES S1 AND S2 IN ANOTHER OPAQUE SURFACE A SCREEN XY WAS ARRANGED IN FRONT OF THE PIN HOLES S1 AND S2 HE OBSERVED A FEW COLOURED BRIGHT AND DARK INTERFERENCE BANDS ON THE SCREEN TO OBTAIN A LARGE NUMBER OF CLEAR BRIGHT AND DARK INTERFERENCE BANDS THE SUN LIGHT IN THE EXPERIMENT WAS REPLACED BY MONOCHROMATIC LIGHT AND THE PIN HOLES WERE REPLACED BY NARROW SLITS S X Y MAXIMUM MAXIMUM MAXIMUM MINIMUM MINIMUM MINIMUM MINIMUM S2 S1 FIGURE 1 1 YOUNG S DOUBLE SLIT EXPERIMENTAL SET UP TEXT BOOK OF PHYSICS 2 EXPLANATION OF INTERFERENCE TH E INTERFERENCE HAS BEEN EXPLAINED BASED ON THE WAVE THEORY OF LIGHT AS LIGHT PASSES THROUGH THE PIN HOLE S SPHERICAL WAVE FRONTS SPREAD OUT AS SHOWN IN FIG 1 1 TH E SOLID CURVES REPRESENT CRESTS AND DOTTED CURVES REPRESENT TROUGHS ON THE WAVES ACCORDING TO HUYGEN S WAVE THEORY EVERY POINT ON THE SURFACE OF THE WAVE FRONT ACTS AS A SOURCE OF SECONDARY WAVELETS AS THE WAVE FRONT SPREADS TO PIN HOLES S1 AND S2 THE WAVE FRONT AT S1 AND S2 ACT AS SECONDARY SOURCES TH E RADII OF THESE SECONDARY WAVE FRONTS INCREASE AS THEY GO AWAY FROM S1 AND S2 AND SUPERIMPOSE TO PRODUCE INTERFERENCE AT A POINT IF A CREST OF ONE WAVE FALLS ON THE CREST OF ANOTHER WAVE OR A TROUGH OF ONE WAVE COMBINES WITH A TROUGH OF ANOTHER WAVE THEN THE AMPLITUDE OF THE RESULTANT WAVE IS THE SUM OF AMPLITUDES OF THE TWO CRESTS OR TROUGHS TH IS CAUSES CONSTRUCTIVE INTERFERENCE AT THAT POINT AND A BRIGHT INTERFERENCE FRINGE IS OBSERVED AT THAT POINT ON THE OTHER HAND IF A CREST OF ONE WAVE FALLS ON THE TROUGH OF ANOTHER WAVE THEN DESTRUCTIVE INTERFERENCE TAKES PLACE AT THAT POINT AND THE RESULTANT AMPLITUDE AT THAT POINT IS MINIMUM SO A DARK INTERFERENCE FRINGE IS OBSERVED AT THAT POINT SINCE THE INTENSITY I OF LIGHT IS PROPORTIONAL TO SQUARE OF AMPLITUDE I R2 THE INTENSITY IS LARGE AT THE PLACES WHERE CONSTRUCTIVE INTERFERENCE TAKES PLACE AND THE INTENSITY IS MINIMUM AT THE PLACES WHERE DESTRUCTIVE INTERFERENCE TAKES PLACE ON THE SCREEN A LARGE NUMBER OF ALTERNATIVELY BRIGHT AND DARK INTERFERENCE BANDS OR FRINGES OF EQUAL WIDTH ARE OBSERVED ANALYTICAL TREATMENT OF INTERFERENCE AS SHOWN IF FIG 1 2 A SOURCE OF MONOCHROMATIC LIGHT OF WAVE LENGTH IS PASSED THROUGH A PIN HOLE S SPHERICAL WAVE FRONTS WERE DIVERGE AND PASS THROUGH THE PIN HOLES S1 AND S2 TH E WAVE FRONTS IN THE PIN HOLES S1 AND S2 ACT AS A SOURCE OF SECONDARY WAVELETS TH E SECONDARY WAVE FRONTS FROM S1 AND S2 COMBINE TO PRODUCE AN INTERFERENCE PATTERN ON THE SCREEN XY NOW WE WILL DETERMINE THE INTENSITY OF INTERFERENCE FRINGE AT A POINT P ON THE SCREEN TH E SCREEN IS AT A DISTANCE OF D FROM S1 AND S2 FIGURE 1 2 SCHEMATIC REPRESENTATION OF INTERFERENCE DUE TO TWO SLITS S1 S2 S M P Q O R SCREEN Y X D X 2D TEXT BOOK OF PHYSICS 3 LET THE AMPLITUDES OF THE WAVES FROM S1 AND S2 BE A1 AND A2 LET THE PHASE DI ERENCE BETWEEN THE WAVES AT P BE SUPPOSE THAT Y1 AND Y2 ARE THE DISPLACEMENTS OF THESE WAVES AT P TH EN Y1 A1 SIN T 1 1 AND Y2 A2 SIN T 1 2 TH ESE TWO WAVES COMBINE TO PRODUCE A RESULTANT WAVE HAVING DISPLACEMENT Y GIVEN AS Y Y1 Y2 A1 SIN T A2 SIN T A1 SIN T A2 SIN T COS A2 COS T SIN SIN T A1 A2 COS COS T A2 SIN 1 3 LET R COS A1 A2 COS 1 4 AND R SIN A2 SIN 1 5 SUBSTITUTING EQUATIONS 1 4 AND 1 5 IN 1 3 WE GET Y SIN T R COS COS T R SIN R SIN T 1 6 EQUATION 1 6 REPRESENTS THE RESULTANT WAVE HAVING AMPLITUDE R TH IS CAN BE OBTAINED BY SQUARING AND ADDING EQUATIONS 1 4 AND 1 5 R R A 2 2 2 2 1 2 COS SIN A A A A 2 2 2 1 2 2 2 2 2 COS COS SIN A A A A 1 2 2 2 2 2 1 2 2 COS SIN COS A A A A 1 2 2 2 1 2 2 COS 1 7 SINCE INTENSITY I OF LIGHT IS EQUAL TO SQUARE OF AMPLITUDE EQUATION 1 7 REPRESENTS THE INTENSITY OF LIGHT AT P HENCE I R A A A A 2 1 2 2 2 1 2 2 COS 1 8 TH E PHASE DI ERENCE BETWEEN THE TWO WAVES AT P CAN BE REPRESENTED IN TERMS OF PATH DI ERENCE AS 2 PATHDIFFERENCE 2 S P S P 2 1 1 9 BASED ON THE PHASE OR PATH DI ERENCE WE SEE THE FOLLOWING SPECIAL CASES FOR INTENSITY OF INTERFERENCE FRINGES CASE 1 CONDITION FOR MAXIMUM INTENSITY FOR MAXIMUM INTENSITY COS 1 IN EQUATION 1 8 THEN 0 2 4 2N WHERE N 0 1 2 OR THE PATH DI ERENCE S2P S1P N TH EN THE INTENSITY OF LIGHT AT P IS I M AX A A A A A A 1 2 2 2 1 2 1 2 2 2 TEXT BOOK OF PHYSICS 4