Class XII - Physics Wave Optics Chapter-wise Problems. Chapter 10

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1 Class XII - Physics Wave Optics Chapte-wise Poblems Answes Chapte (c) (a) 3 (a) 4 (c) 5 (d) 6 (a), (b), (d) 7 (b), (d) 8 (a), (b) 9 (a), (b) Yes Spheical Spheical with huge adius as compaed to the eath s adius so that it is almost a plane 3 Sound wave have fequencies Hz to khz The coesponding wavelengths ae 5m and 5mm, espectively iffaction effects ae seen if thee ae slits of width a such that α : Page of 8

2 Fo light waves, wavelengths 7 m Thus diffaction effects will show when 7 a : m wheeas fo sound they will show fo 5mm < a < 5m 4 The linea distance between two dots is l 54 cm ; 84 cm 3 At a distance of Z cm this subtends an angle l 84 cm φ : l / z z : 45 cm 4 φ 58 5 Only in the special cases when the pass axis of (III) is paollel to (I) o (II) thee shall be no light emeging In all othe cases thee shall be light emeging because the pass axis of (II) is no longe pependicula to the pass axis of (III) 6 Polaisation by eflection occus when the angle of incidence is the n Bewste s angle ie tanθ B whee n < n n When light tavels in such a medium the citical angle is whee n < n As tan θ B > sin θ c fo lage angles, θb < θc Thus, polaisation by eflection shall definitely occu n sinθ c n 7 d sin β whee β is the angle subtended by the objective at the object Fo light of 55 A o d 7 55 m sin β Fo electons acceleated though V the deboglie wavelength is h p 7 3nm 3 9 m 3 d ' sin β Page of 8

3 3 d ' sin β d ' 3 : 7 d 55 8 T P + x, T P x 3 S P (S T ) + (PT ) [ + ( x) ] / S P [ + ( + x) ] / Minima will occu when [ + ( + x) ] / [ + ( x) ] / If x ( + 4 ) / (5 ) /, 5 9 Without P: A A + A ω ω φ A A + A A sin( kx t)+a sin( kx t + ) A A + A () () A A [sin( kx wt) + sin( kx ωt + φ] whee A, polaizations Intensity A ae the amplitudes of eithe of the beam in and { + } ( ) A A [sin kx wt (+cos φ + sin φ)+sin ( kx ωt) sin φ] { A } A + (+cos φ ) aveage Page 3 of 8

4 aveage aveage A ( + cos φ)since A A With P: Assume A is blocked: Intensity (A + A ) + (A ) ( cos φ) A A + + Given: I 4 A Intensity without polaise at pincipal maxima Intensity at pincipal maxima with polaise A + 5 I 8 Intensity at fist ima with polaise A A ( ) + I 8 Path diffeence d sin θ + ( µ ) l Fo pincipal maxima, d sinθ + 5l l d sinθ Q l 4d 6 4 OP tan θ 6 Fo the fist ima: d sin θ +5 l ± Page 4 of 8

5 ± / 5 l ± / /8 sin θ ± d 4 6 On the positive side: 3 sinθ + 6 On the negative side: 5 sin θ 6 The fist pincipal maxima on the positive side is at distance + sinθ 3 tanθ + above O sin θ 6 3 In the ve side, the distance will be 5 tanθ below O 6 5 (i) Conside the distubances at R which is a distance d fom A Let the wave at R because of A be Y A a cos ωt The path diffeence of the signal fom A with that fom B is / and hence the phase diffeence is π Thus the wave at R because of B is y a cos( ωt π ) a cos ωt B R The path diffeence of the signal fom C with that fom A is and hence the phase diffeence is π Thus the wave at R because of C is y c a cos ωt The path diffeence between the signal fom with that of A is / / R A B C / d + ( d /) / d + d + 4d / d + d + 8d If d >> the path diffeence is π : and hence the phase diffeence Page 5 of 8

6 y a cosωt Thus, the signal picked up at R is y A + y B + y C + y Let the signal picked up at R fom B be y B a cos ωt The path diffeence between signal at and that at B is / y a cosωt The path diffeence between signal at A and that at B is ( ) + / d + d d d 4d : 8 d The phase diffeence is π π φ : 8 d 4d Hence, y A a cos (ωt-φ) Similaly, y C a cos (ωt-φ) Signal picked up by R is y A + y B + y C + y y a cos (ωt-φ) y 4a cos ( ωt φ) I a Thus R picks up the lage signal (ii) If B is switched off, R picks up y a cos ωt I R a R picks up y a cos ωt IR a Thus R and R pick up the same signal (c) If is switched off R picks up y a cos ωt IR a R picks up y 3a cos ωt IR 9 a Thus R picks up lage signal compaed to R (iv)thus a signal at R indicates B has been switched off and an enhanced signal at R indicates has been switched off Page 6 of 8

7 (i) Suppose the postulate is tue, then two paallel ays would poceed as shown in Fig Assug E shows a wave font then all points on this must have the same phase All points with the same optical path length must have the same phase E i Fig A i B i C ai medium Thus ε µ AE BC ε µ C o BC ε µ ( C AE ) BC >, C > AE As showing that the postulate is easonable If howeve, the light poceeded in the sense it does fo odinay mateial (viz in the fouth quadant, Fig ) Then ε µ AE BC ε µ C A Fig E B C ai medium o, BC ε µ ( C AE ) As AE > C, BC < O showing that this is not possible Hence the postalate is coect (ii) Fom Fig BC AC sin θ i and C-AE AC sin θ : Since ε µ ( AE C) BC n sin θ sin θ i 3 Conside a ay incident at an angle i A pat of this ay is eflected fom the ai-film inteface and a pat efacted inside This is patly eflected at the film-glass inteface and a pat tansmitted A pat of the eflected ay is eflected at the film-ai inteface and a pat tansmitted as paallel to Of couse succesive eflections and tansmissions will keep on deceasing the amplitude of the wave Hence ays and shall doate the behavio If incident light is to be tansmitted though the lens, and should intefee destuctively Both the eflections at A and ae fom lowe to highe efactive index and hence thee is no phase change on eflection The optical path diffeence between and is n (A + C) AB If d is the thickness of the film, then A C d cos AB AC sini AC d tan AC d tan Hence, AB d tan sini Thus the optical path diffeence is Page 7 of 8

8 d n d tan sini cos sini d sin d sini sin cos cos sin d sin sin cos Ai n Film n 38 Glass n 5 i A B i C nd cos Fo these waves to inteefee destuctively this must be / nd cos o nd cos /4 Fo a camea lens, the souces ae in the vetical plane and hence i nd ; 4 55 A d ; 38 4 o o A Page 8 of 8

This brief note explains why the Michel-Levy colour chart for birefringence looks like this...

This brief note explains why the Michel-Levy colour chart for birefringence looks like this... This bief note explains why the Michel-Levy colou chat fo biefingence looks like this... Theoy of Levy Colou Chat fo Biefingent Mateials Between Cossed Polas Biefingence = n n, the diffeence of the efactive