λ = ) = d sin! n Analysis: Rearrange the equation dsinθn to solve for wavelength; # d sin! n = n " 1 & $ ( ) n " 1 2 Solution: ( m) sin 3.

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1 Sectio 9.5: Iterferece of ight Waves: Youg s Double-Slit Eperimet Tutorial Practice, page 82. Give: ouble-slit iterferece; 5; θ ; 0.02 mm m Require: λ siθ λ to solve for wavelegth; si! & ( ) ) si! 2 siθ λ 2 5 (.2 ) si λ 6.2 Statemet: The wavelegth of the moochromatic light is m. 2. Give: ouble-slit iterferece; mm m; λ 650 m m; 2.6 m Require: Δ, at the cetre of the iterferece patter Aalysis: Δ Δ (2.6 m)(6.5 ) Δ 3. cm Statemet: The frige separatio at the cetre of the iterferece patter is 3. cm. 3. Give: ouble-slit iterferece; 3; λ 652 m m; m Require: θ 3 siθ λ to solve for the agle of the frige; Copyright 202 Nelso Eucatio t. Chapter 9: Waves a ight 9.5-

2 si! & ( ) & &! si ( ) ( ' ( & &! si ( ) ( ' ( 3 & & si ( (6.52 *0 7 m )( ( 6.3*0 6 m '! 3 5 Statemet: The frige is observe at the agle 5. Mii Ivestigatio: Wavelegths of ight, page 83 A. Both iterferece patters cosiste of a horizotal ba of light fille with coloure a ark vertical friges. The friges were closer together with the gree filter tha with the re filter. B. Table : Number of ies betwee Two Sliers Number of lies fou betwee two sliers Colour of light re 9 gree C. Table 2: Calculatig the Wavelegth of ight Re light Gree light (m).0.0 (m) (m) Δ (m) λ (m) Sample calculatio: Δ λ Δ λ λ The wavelegth is. 0 7 m. 3 (.76 )(2.5 )..0 m Copyright 202 Nelso Eucatio t. Chapter 9: Waves a ight 9.5-2

3 Sectio 9.5 Questios, page 8. Aswers may vary. Sample aswer: Whe all other factors are kept costat, the friges for the re light, λ 650 m, are more wiely space tha the friges for the blue light, λ 70 m. 2. Give: ouble-slit iterferece; 0.20 mm m; 3.5 m; ark frige;.6 mm m Require: λ λ! & ( (.6 )03 m)(2.0 )0 m) & ( (3.5 m) 5.3)0 7 m to solve for wavelegth;! 530 m Statemet: The wavelegth of the light is 530 m. 3. Aswers may vary. Sample aswer: A uerwater ouble-slit eperimet woul have ifferet results tha a ouble-slit eperimet i air because, i water, the spee of light is slower a the wavelegth is shorter. The spacig betwee the resultig friges woul be closer together uerwater tha i air. Copyright 202 Nelso Eucatio t. Chapter 9: Waves a ight 9.5-3

4 . Give: ouble-slit iterferece; Require: ; λ.5! 2& ' (! 2& ' (! 2& ' ( (2.8 ) 0!2 m)(3.0 ) 0! m) 5! 2& ' (.5 ) 0!7 m) 0.30 mm 3.0 ; 5 ark frige; to solve for istace to the scree; 9 m Statemet: The istace at which the scree is place is 9 m. 5. (a) Give: ouble-slit iterferece; 0.5 mm.5 0 m; 2.0 m; 3 Δ 0.56 cm 5.6 Require: λ Δ to solve for wavelegth Δ λ 3 (.5 )(5.6 ) (2.0 m) λ.2 Statemet: The wavelegth of the source is m, or 20 m. (b) Give: ouble-slit iterferece; 0.5 mm.5 0 m; 2.0 m; λ 600 m 6 Require: Δ, of the ark friges Aalysis: Δ Copyright 202 Nelso Eucatio t. Chapter 9: Waves a ight 9.5-

5 ! (2.0 m)(6 07 m) (.50 m)! m Statemet: The spacig of the ark friges is m, or 0.8 cm. 6. Give: ouble-slit iterferece; 2 ark friges;! 2 5. Require: λ siθ λ 2 λ siθ 2 λ siθ siθ λ to solve for ; λ 2 2 si 5. 6 λ Statemet: The ratio of the separatio of the slits to the wavelegth is 6:. 7. (a) Give: ouble-slit iterferece; 0.80 mm m; 9 cm 0.9 m; Δ Require: λ 0.33 mm 3.3 Δ Δ λ Δ to solve for wavelegth; Copyright 202 Nelso Eucatio t. Chapter 9: Waves a ight 9.5-5

6 Δ Δ λ (8.0 )(3.3 ) (0.9 m ) λ 5.39 (oe etra igit carrie) λ 5. Statemet: The wavelegth of the moochromatic light is m, or 50 m. (b) Give: ouble-slit iterferece; 0.60 mm m; 0.9 m; λ m Require: Δ, of the ark friges Aalysis: Δ Δ (0.9 m)(5.39 ) (6.0 ) Δ. Statemet: The spacig of the ark friges is. 0 m, or 0. mm (a) Give: ouble-slit iterferece; 2.5 m; λ 5. ; Δ 2 mm.2 Require: Δ to solve for istace betwee the slits; Δ Δ Δ (2.5 m)(5. ) 2 (.2 ). Statemet: The slit spacig is. 0 m, or 0. mm. (b) Solutios may vary. Sample solutio: From Δ, the frige separatio is iversely proportioal to the slit spacig. If the slit spacig is reuce by a factor of three, the frige separatio will icrease by a factor of three. The frige separatio will chage to 3 2 mm 36 mm, or 3.6 cm. Copyright 202 Nelso Eucatio t. Chapter 9: Waves a ight 9.5-6

7 9. Aswers may vary. Stuet aswers shoul iclue some of the followig poits. Newto evelope a particle theory of light that eplaie rectiliear propagatio a reflectio well. His reputatio put the work of others at the time i the shaows. Grimali was workig o a theory for the iffractio a ispersio of light, a Hooke was lookig a wave theory. ater, Newto s theory that light travelle faster i a meium tha i a vacuum was show eperimetally to be icorrect. With this failure, Newto s eplaatios of refractio, colour, a ispersio were also refute. Huyges wave ieas a Youg s ouble-slit iterferece eperimet showe that light is efiitely a wave. By 900, all kow properties of light coul be eplaie by a wave moel. Copyright 202 Nelso Eucatio t. Chapter 9: Waves a ight 9.5-7

refracted and the wavelength of the light shortens. According to the equation! = w"y L

$refracted and the wavelength of the light shortens. According to the equation! = wy L$ Sectio 10.2: Sigle-Slit Diffractio Tutorial 1 Practice, page 516 1. Whe light travels from air to a medium that is deser tha air, such as ater, the light is refracted ad the avelegth of the light shortes.