12 Superposition Tutorial

m issing . 5 15 E xplain w hy certain orders of the interference pattern of a diffraction grating are 5 14 S tate the R ayleigh criteń on for im age resolution. E xplain your sym bo©¥s c©¥early . diffraction pattern occur. W hat condition is necessary for the expression to be valid? 5 13 S tate the expression w hich gives the angles at w hich the m inim a of a singl©¡s©¥it beam of m onochrom atic light passes through a diffraction grating? 5 12 H ow do you calcu©¥ate the m axim um num ber of orders that can be observed w hen a in its derivation. 5 11 W hat is the grating form ula? D efine the sym bo©¥s used and state the assum ption used w hat conditions w ou©¥d the equation provide an accurate value of ¡¿? n the w avelength Ä , the slit separation a and the slit to screen distance D ' ? U n d e r In a Y oung ' s doub©¥s©¥it experim ent, w hat is the re©¥ation betw een the fringe separation5 10 interference pattern, but sound from tw o loudspeakers can. 5 9 E xplain w hy light from tw o m onochrom atic sources do not produce an observab©¥e observable? 5 8 W nat are the necessary conditions for two - source interference pattern to be interfenence? 5 7 W nat do you understand by the term s coherence, a n d constructive and destï uctive straight ©¥ine . ) 5 6 W ny is diffraction of ©¥ight not easily observed? (lt w as thought that light trave©¥s in a aperture is reduced or w hen it is enlarged? 5 5 W nat is diffraction? ls the enect of diffraction m ore pronounced w hen the size of the closed and w ith both ends open? both ends? W hat about that of a stationary sound w ave set up in a pipe w ith one end 5 4 W nat is the longest possib©¥e w avelength of a stationary w ave aot up In a string fixed at of a stationary w ave? H ow about their am p©¥￠tudes? 5 3 W nat is the phase difference betw een parlic©¥es located betw een tw o adjacent nodes 5 2 H ow ls a stationary w ave form ed? 5 1 W nat ls the princip©¥e of ©¥uperposition? 国 号 E e©¥f- C hock Q ue©¥t©¥ons ìé Ûý£º12 S U P E R P O S IT IO N .. - . . .. T utorial

(c) the num ber of ditftaction m axim a observed. (b) the angle to the norm al at w hich the first order m axim um is seen, (a) the grating spacing , m onochrom atic ©¥ight of w ave©¥ength 6 0 0 nm . C alculate S P 6 A diffraction grating has 4 0 0 lines per m m and is il©¥um inated norm a©¥ly by 0 ¡¤ (c) W nat can be said about the fringe separation betw een higher order fringes? Oi) the screen is m oved closer to the slits? (i) the separation of the slits is decreased? (b) W hat is the effect on the appearance of the fringes if (a) W hat is the separation of the fringes on the screen? 1 . 2 m . w here the slits separation is 0 . 40 m m and the distance of the s©¥its to the screen is R ed ©¥ight of wavelength 6 . 0 ¡¿ 1 0 4 m is incident norm ally on a Y oung ' s doub©¥e - s lit, S P 5 of the w aves? the detector detected zero intensity w ere ©¥ocated 1 . 5 cm apart. W hat is the frequency m icrow ave detector is traversed along the standing wave, s u c c e s s ive points at w nich rellected w ave and the incident w ave superpose to form a standing wave. W hen a A m icrow ave transm itter em its w aves w hich are rellected from a m eta©¥ p©¥ate . T heS P 4 sound ©¥n air ls 3 0 0 m s - 1 , determ ine the two lowest resonant frequencies. S P 3 A n organ pipe of e¨¤ective length 0 . 60 m ©¥s closed at one end . G iven that the epeed of Oi) W r©¥at ls the speed of the transverse w aves In the string in term s of ￠a and L ? (I) W r©¥at l8 the ratio ￠zlf,? first overtone frequency fz ls also produced . fundam enta©¥ note of frequency f. . W nen the string l8 plucked al a different point, the A string of length L , fixed at both enda, l8 pktcked at H s m idpoint w xl em its it©¥ S p2 J8 ó©¥1©¥12 resonant vibrations at it©¥ fundam ental frequency . of the bridge ls 4 0 0 m s - 1 , C alculate the leng©¥h of tt©¥e bridge when ©¥here ©¥©¥ danger of gust at S ©¥ In©¥erva©¥s. ©¥l ia es©¥im a©¥ed ©¥hat lhe ©¥peed of transverse w aves t©¥long the apan A suspension bridge il ©¥D be built au oss a valley where i©¥ I©¥ known ©¥H M winda canS P 1 S elf- P ractice Q uoat©¥ons Y E A R 5 ¡¤ 6 P H Y S ©¥C S D E P A R T M E RdT R A F F L E S IF S T ©¥T uT IO N

D Ä Àla C Ä Àt2 a B À/2 Àla A 1/2 1}2 a S P - R P sin Q 爿 ´Ì Ï¢ P Jnd for sin O ? W hich of the follow ing gives the correct expressions for the path di¨¤erence S P - R P i m akes an angle ©¢with the direction of the incident light as show n below . a. T he di¨¤raction pattern is form ed on a screen P Q . T he first m inim um of this pattern M onochrom atic light of w avelength À is incident norm ally on a single s©¥it R S of w idthS P 1 0 C ©¥l. 6 ¡¿©¥0 9 J7 7 /ï U ©¥4 B 9 . 6 ¡¿10 E 2 . 3 ¡¿10￠ A 5 . 8 ¡¿10 3 D ©¥9 . 2 x los m c©¥re are there on the grating? from the direction oí the incident bc©¥m H ow m any ©¥ines per second onder rpectrum is di©¥T ractcd through an angle of 6 op diffraction grating . T hc m ost devi©¥ted w avelcnsth in the 4 . 5 ¡¿ ©¥ī m 1o 7 . 5 ¡¿ ©¥? m » ls incident norm al©¥y on a A p©¥r©¥©¥le©¥ beam of w hl©¥e lisht (range of w avelengths S P 9 国 号 J86N ©¥©¥ : N 99/U ©¥ ©¥ E (l©¥ ¡ß l)) - (l©© ¡ß ©©©¥) = n©¥©¥ N 8 0 M n D (l©¥ ¡ß li) - ¡¶l©© ¡ß \ ) - ( 2 n©¥ ¡ß ©¥) M 2 C (1) - U = m k B «t) - l4 ) - ( 2 m ¡ß I ) 2 A (t©¥ - l ©©) . ( 2 n ©¥ ¡ß ©¥) 2 condition for deitruc©¥iw ©¥nterfem ce « q ©¥©¥ ©¥h©¥t allowed to r©¥l©¥ on a ©¥crecn. ©¥n d ©¥r n ©¥ ©¥©¥ ©¥ p o ©¥©¥tlv e I n ©¥e l er . h ©¥ ©¥$ show n ln the diagram ©¥bovc (R * 3 ), th e ©¥i￠ M ©¥©¥ ©¥h ©¥crņ to of w ave©¥cng©¥h ©¥ rrom a ©¥n ln©¥ ©¥outce P . T w o idcn©¥lca©¥ nan ow * ©¥lt©¥ S , ©¥nd S t « e lllum ©¥n« txl bp ll©¥h©¥ S P 7 Y E A R S - 6 P H Y S ©¥C S D E P A R T M E R4 T R A F F L E S ©¥N S T IT U T Iot¨©

4 (b) the lowest frequency at which the tube w ill resonate w hen it is open at both ends. (a) the end - correction, a n d observed w hen the length of air colum n is 4 8 . 0 cm . D eterm ine 5 12 H z w hen the air co©¥um n above the w ater level is 1 4 . 8 cm . T he next resonance is w ater. A s it is raised, the tube first resonates to a vibrating tuning - fork of frequency A 60 . 0 cm long, v e rtica©¥ hollow tube is initially subm erged just below the surface of * equencies of vibration of the oscil©¥ator, (c) E xplain why a stationary w ave is observed on the string only at particular (b) O n your diagram , ©¥abel the position of nodes N on the string . the w ave on the string . distance between the oscillator and the pul©¥ey corresponds to tw o w avelengths of (a) D raw the stationary w ave on the string when the frequency is sucH that the string at certain frequencies. A s the frequency of the oscillator is increased, stationary w aves are produced on the ß¾ ìé ¡á Ù³ over a pulley . T he string is kept under tension by m eans of a w eight as show n below . O ne end of a horizontal string is a« ached to an oscillator and the other end is passed D 1 J 99/3/4 stationary w aves D iscussion Q uestions increased . D the intensities of a[l the peaks decreased and the w idth of the pattern pattern increased. C the intensities of alt the peaks rem ained unchanged and the w idth of the decreased . B the intensities of aïl the peaks decreased and the w idth of the pattern unchanged . A the intensities of all the peaks decreased and the w idth of the pattern rem ained S P IL W ith reference to S P 1 0 , w hen the w idth of the slit is reduced , Y E A R 5 - 6 P H Y S IC S D E P A R T M E N T R A F F L E S t N S T IT U T IO N

5 S uggest suitab©¥e va©¥ues for d and D . separation s are form ed on the screen. S tate the re©¥ation betw een Ä , s , d, a nd D . and produces fringes on the screen. W ith light of w avelength Ä , bright fringes of S illum inates a narrow slit A , w hich acts as a source for the narrow s©¥its B and C , T he figure above illustrates the Y oung ' s