# 4.A: diffraction (Majibu)

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## Angalia Uelewa Wako

4.1. $$\displaystyle 17.8°, 37.7°, 66.4°$$; hapana

4.2. $$\displaystyle 74.3°, 0.0083I_0$$

4.3. Kutoka$$\displaystyle dsinθ=mλ$$, upeo wa kuingiliwa hutokea$$\displaystyle 2.87°$$ kwa$$\displaystyle m=20$$. Kutoka Equation 4.1, hii pia ni angle kwa kiwango cha chini cha pili cha diffraction. (Kumbuka: Equations zote mbili hutumia index m lakini zinarejelea matukio tofauti.)

4.4. $$\displaystyle 3.332×10^{−6}m$$au mistari 300 kwa milimita

4.5. $$\displaystyle 8.4×10^{−4}rad$$, 3000 mara pana kuliko darubini ya Hubble

4.6. $$\displaystyle 38.4°$$na$$\displaystyle 68.8°$$; kati ya$$\displaystyle θ=0°→90°$$, amri 1, 2, na 3, ni wote zilizopo.

## Maswali ya dhana

1. Mfano wa diffraction unakuwa pana.

3. Walkie-talkies hutumia mawimbi ya redio ambayo wavelengths yake ni sawa na ukubwa wa kilima na hivyo wanaweza kutofautiana karibu na kilima. Wavelengths inayoonekana ya tochi ya kusafiri kama mionzi kwa kiwango hiki cha ukubwa.

5. Mfano wa diffraction unakuwa mbili-dimensional, na pindo kuu, ambazo sasa ni matangazo, zinaendesha kwa maelekezo ya perpendicular na matangazo ya kukata tamaa katika maelekezo ya kati.

7. Kipimo$$\displaystyle β=ϕ/2$$ ni angle ya arc iliyoonyeshwa kwenye mchoro wa phasor katika Mchoro 4.7. Tofauti ya awamu kati ya wavelet ya kwanza na ya mwisho ya Huygens katika mtego mmoja ni$$\displaystyle 2β$$ na inahusiana na ukingo wa arc ambayo huunda awamu ya matokeo ambayo huamua kiwango cha mwanga.

9. bluu; wavelength mfupi ya matokeo ya mwanga wa bluu katika angle ndogo kwa kikomo cha diffraction.

11. Hapana, umbali huu ni amri tatu za ukubwa mdogo kuliko wavelength ya mwanga inayoonekana, mwanga unaoonekana hufanya uchunguzi maskini kwa atomi.

13. Wavelengths ya UV ni kubwa zaidi kuliko nafasi ya kimiani katika fuwele kama kwamba hakuna diffraction. Ulinganifu wa Bragg unamaanisha thamani ya sinkubwa kuliko umoja, ambayo haina suluhisho.

15. Image itaonekana katika eneo tofauti na/au ukubwa wakati kutazamwa kwa kutumia wavelength$$\displaystyle 10%$$ mfupi lakini katika nusu ya wavelength hasa, kuingiliwa juu-ili reconstructs picha ya awali, rangi tofauti.

## Matatizo

17. a$$\displaystyle 33.4°$$;.

b. hapana

19. a$$\displaystyle 1.35×10^{−6}m$$;.

b.$$\displaystyle 69.9°$$

21. 750 nm

23. 2.4 mm, 4.7 mm

25. a$$\displaystyle 1.00λ$$;.

b$$\displaystyle 50.0λ$$;

c.$$\displaystyle 1000λ$$

27. 1.92 m

29. $$\displaystyle 45.1°$$

31. $$\displaystyle I/I_0=2.2×10^{−5}$$

33. $$\displaystyle 0.63I_0,0.11I_0,0.0067I_0,0.0062I_0,0.00088I_0$$

35. 0.200

37. 3

39. 9

41. $$\displaystyle 5.97°$$

43. $$\displaystyle 8.99×10^3$$

45. 707 nm

47. a$$\displaystyle 11.8°, 12.5°, 14.1°, 19.2°$$;.

b.$$\displaystyle 24.2°, 25.7°, 29.1°, 41.0°$$; c Kupunguza idadi ya mistari kwa sentimita kwa sababu ya x ina maana kwamba angle kwa kiwango cha juu cha x-ili ni sawa na angle ya awali kwa kiwango cha juu cha kwanza.

49. a. kutumia$$\displaystyle λ=700nm,θ=5.0°$$;

b. kutumia$$\displaystyle λ=460nm,θ=3.3°$$

51. a. 26,300 mistari/cm;

b. ndiyo;

c. hapana

53. $$\displaystyle 1.13×10^{−2}m$$

55. 107 m

57. a$$\displaystyle 7.72×10^{−4}rad$$;.

b. 23.2 m;

c. 590 km

59. a$$\displaystyle 2.24×10^{−4}rad$$;.

b. 5.81 km;

c. 0.179 mm;

d. inaweza kutatua maelezo 0.2 mm mbali na urefu wa mkono

61. $$\displaystyle 2.9μm$$

63. 6.0 cm

65. 7.71 km

67. 1.0 m

69. 1.2 cm au karibu

71. hapana

73. 0.120 nm

75. $$\displaystyle 4.51°$$

77. $$\displaystyle 13.2°$$

79. a. 2.2 mm;

b.$$\displaystyle 0.172°$$, pili ili njano na ya tatu ya violet sanjari

81. 2.2 km

83. 1.3 cm

85. a. 0.28 mm;

b. 0.28 m;

c. 280 m;

d. 113 km

87. 33 m

89. a. wima;

b$$\displaystyle ±20°, ±44°$$;

c$$\displaystyle 0, ±31°, ±60°$$;

d. 89 cm;

e. 71 cm

91. 0.98 cm

93. $$\displaystyle I/I_0=0.041$$

95. 340 nm

b. 480 nm na 660 nm

99. amri mbili

101. ndiyo na N/A

103. 600 nm

105. a$$\displaystyle 3.4×10^{−5°}$$;.

b.$$\displaystyle 51°$$

107. 0.63 m

109. 1

111. $$\displaystyle 0.17 mW/cm^2$$kwa$$\displaystyle m=1$$ tu, hakuna amri ya juu

113. $$\displaystyle 28.7°$$

115. a. 42.3 nm;

b. wavelength hii si katika wigo inayoonekana.

c. idadi ya slits katika grating hii diffraction ni kubwa mno. Kuunganisha katika nyaya zilizounganishwa kunaweza kufanywa kwa azimio la nm 50, hivyo kutenganishwa kwa nm 400 ni kikomo cha kile tunaweza kufanya leo. Nafasi hii ya mstari ni ndogo mno ili kuzalisha diffraction ya mwanga.

117. a. 549 km;

b Hii ni darubini kubwa isiyo na maana.

c Ni busara kudhani kikomo cha diffraction kwa telescopes za macho isipokuwa katika nafasi kutokana na athari za anga.

## Changamoto Matatizo

119. a$$\displaystyle I=0.00500I_0,0.00335I_0$$;.

b.$$\displaystyle I=0.00500I_0,0.00335I_0$$

121. 12,800

123. $$\displaystyle 1.58×10^{−6}m$$