Chapter 9 answers. Section 9.1. Worked example: Try yourself Heinemann Physics 12 4e APPLYING HUYGENS PRINCIPLE

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1 Chapter 9 answers Heinemann Physics 12 4e Section 9.1 Worke example: Try yourself APPLYING HUYGENS PRINCIPLE On the circular waves shown below, sketch some of the seconary wavelets on the outer wavefront an raw the appearance of the new wave forme after 1 perio. Sketch a number of seconary wavelets on the avancing wavefront. Sketch the new wavefront.

2 Worke example: Try yourself CALCULATING REFRACTIVE INDEX The spee of light in crown glass is m s 1. Given that the spee of light in a vacuum is m s 1, calculate the refractive inex of crown glass. Recall the efinition of refractive inex. n c v Substitute the appropriate values into the formula an solve. n Worke example: Try yourself SPEED OF LIGHT CHANGES A ray of light travels from water (n 1.33) where it has a spee of m s 1 into glass (n 1.85). Calculate the spee of light in glass. Recall the formula. n 1 v 1 n 2 v 2 Substitute the appropriate values into the formula an solve v v v m s 1 Worke example: Try yourself USING SNELL S LAW A ray of light in air strikes a piece of flint glass (n 1.62) at angle of incience of 50 to the normal. Calculate the angle of refraction of the light in the glass. Recall Snell s law. n 1 n 2 Recall the refractive inex of air. n Substitute the appropriate values into the formula to fin a value for sin Calculate the angle of refraction. θ 2 sin Worke example: Try yourself CALCULATING CRITICAL ANGLE Calculate the critical angle for light passing from iamon into air. Recall the equation for critical angle. sin θ c n 2 n 1 Substitute the refractive inexes of iamon an air into the formula. sin θ c Solve for θ c. θ c sin

3 9.1 review 1 a wave moel b wave moel c particle moel 2 C. Newton s esteeme reputation meant that his theory was regare as correct. 3 The new wavefront shoul be a straight line across the front of the seconary wavelets. rays giving irection of propagation new wavefront initial wavefront 4 Therefore, the spee of light in seawater will be slower than in pure water. 5 Recall the efinition of refractive inex: n c v Rearrange to get v c n m s 1 6 n 1 v 1 n 2 v n n Recall Snell s law: n 1 n sin sin θ 2 sin Total internal reflection occurs when light passes from a more-ense meium into a less-ense meium an refracts away from the normal. a no b yes c yes no 9 D. Significant iffraction occurs when λ w is approximately 1 or greater. 700 nm 10 6 m an mm or 10 6 m. 10 Polarisation is a phenomenon in which transverse waves are restricte in their irection of vibration. Polarisation can only occur in transverse waves an cannot occur in longituinal waves. Since light can be polarise, it must be a transverse wave.

4 Section 9.2 Worke example: Try yourself CALCULATING WAVELENGTH FROM FRINGE SEPARATION Green laser is irecte through a pair of thin slits that are 25 μm apart. The slits are 1.5 m from a screen on which bright fringes are 3.3 cm apart. Use this information to calculate the wavelength of green light in nm. Recall the equation for fringe separation. Transpose the equation to make λ the subject. Δx λl λ Δx L Substitute values into the equation an solve. λ m Express your answer using the unit specifie. λ 550 nm 9.2 review 1 D. Light passe through the ouble slits to hit the screen. Young s ouble-slit experiment prouce an interference pattern of alternating bright an ark lines on the screen. 2 C an D. As laser light is monochromatic an coherent, it is more likely to prouce the interference pattern expecte in Young s experiment. 3 A an D. When crests meet troughs, the aition of these out-of-phase waves means that they cancel to form a noe. 4 The central antinoe occurs where both waves have travelle the same istance, i.e. the path ifference is 0. The next antinoes on either sie occur when the path ifference is 1λ. Intensity M 5 Up until Young s experiment, most scientists supporte a particle or corpuscular moel of light. Young s experiment emonstrate interference patterns, which are characteristic of waves. This le to scientists abanoning the particle theory an supporting a wave moel of light. 6 Recall the equation for fringe separation: Δx λl a increase b ecrease c increase 7 p n 1 2 λ For the fifth ark fringe, n 5 p λ Therefore, the fifth ark fringe occurs where the path ifference is 4.5λ nm 2610 nm or m 8 Constructive interference occurs when the path ifference is a whole number multiple of the wavelength. Destructive interference occurs when the path ifference is an o number multiple of half the wavelength. a estructive b constructive c estructive

5 9 p nλ For the secon bright fringe, n 2 p 2λ Therefore, the secon bright fringe occurs where the path ifference is nm 10 Δx λl λ Δx L m 455 nm Section 9.3 Worke example: Try yourself USING THE WAVE EQUATION FOR LIGHT A particular colour of re light has a wavelength of 600 nm. Calculate the frequency of this colour. Recall the wave equation for light. Transpose the equation to make frequency the subject. c fλ f c λ Substitute in values to etermine the frequency of this wavelength of light f Hz 9.3 review 1 B. Mechanical waves require a meium whereas light waves can travel through a vacuum. 2 D. Light is electromagnetic raiation that is compose of changing electric an magnetic fiels. Electric an magnetic waves oscillate at 90 to each other, so in an electromagnetic wave the changing electric an magnetic fiels are orientate perpenicular to each other. 3 D. Electromagnetic raiation with a wavelength of 200 nm woul be classifie as ultraviolet light since this part of the spectrum is shorter wavelength than visible light. 4 From shortest to longest wavelength: X-rays, visible light, infrare raiation, FM raio waves. 5 Use c fλ Transpose to make frequency the subject. a re, f c λ Hz b yellow, f Hz c blue, f Hz violet, f Hz % 0.07%

6 7 Use c fλ Transpose to make wavelength the subject. λ c f nm 8 Use c fλ Transpose to make wavelength the subject. λ c f m 9 Use c fλ Transpose to make frequency the subject. f c λ Hz 10 Frequency of microwave oven is 2.45 GHz from text on page 323. Use c fλ Transpose to make wavelength the subject. λ c f m CHAPTER 9 REVIEW 1 A. This shows the bening of the eges of the waves as they pass through a gap. 2 Since Δx λl, the iffraction pattern woul sprea out more from blue to green. The green light (λ 525 nm) has a longer wavelength than blue light (λ 460 nm). Green s longer wavelength results in more wiely space fringes an a wier overall pattern. 3 D. Polarisation is a phenomenon in which transverse waves are restricte in their irection of vibration. Polarisation can only occur in transverse waves an cannot occur in longituinal waves. Since light can be polarise, it must be a transverse wave. 4 Both snow an water reflect light. This reflecte light is known as glare. The light reflecte from water an snow is partially polarise. Both snowboarers an sailors are likely to wear polarising sunglasses as these will absorb the polarise glare from the snow or water respectively. 5 c fλ m s 1 6 As light travels from quartz (n 1.46) to water (n 1.33), its spee increases which causes it to refract away from the normal. 7 A: incient ray B: normal C: reflecte ray D: bounary between meia E: refracte ray

7 8 n 1 n 2 n 2 n sin sin 28.5 Since n c v v c n x 10 8 m s 1 9 Use Snell s law: n 1 n 2 angle a 1.00 sin sin a 1.00 sin 40 sin a a sin 1 (0.4285) 25.4 angle b Since a an b are corresponing angles, a b 25.4 angle c 1.50 sin sin c 1.50 sin 25.4 sin c c sin a The angle of incience is measure with respect to the normal which is rawn at a right angle to the glass air bounary. θ i b n 1 n sin x n sin θ 2 sin c θ θ 2 θ v c n m s 1 11 a re light n 1 n sin sin θ re sin θ re n 1 n sin θ 2 sin

8 b violet light n 1 n sin sin θ violet sin θ violet n 1 n sin 30o θ 2 sin c Δθ θ 2 θ v c n m s n 2 12 θ c sin 1 n a θ c sin b θ c sin c θ c sin B, D, A, C. The bigger the ifference in refractive inexes, the bigger the angle of eviation. The air water bounary has the smallest ifference in refractive inices so it will prouce the smallest angle of eviation. The air iamon bounary has the biggest ifference in refractive inices so it will prouce the biggest angle of eviation. λl 14 a Δx λ Δx L nm b 581 nm is closest to yellow (accoring to Table 9.1.3) 15 A path ifference of 1½ λ correspons to the secon ark ban on each sie of the central maximum at M. Intensity M 16 In orer of ecreasing wavelength: raio waves, microwaves, infrare, visible, ultraviolet, X-rays, gamma rays 17 a microwaves b infrare waves c X-rays 18 Since c fλ λ c f m

9 19 Young performe his famous experiment in 1803, in which he observe an interference pattern in light. Young shone monochromatic light on a pair of narrow slits. Light passe through the slits an forme a pattern of bright an ark lines/fringes/bans on a screen. Young compare this to interference patterns he ha observe, an he ientifie that these lines correspone to regions of constructive an estructive interference. This coul only be explaine by consiering light to be a wave. 20 A microwave oven is tune to prouce electromagnetic waves with a frequency of 2.45 GHz. This is the resonant frequency of water molecules. When foo is bombare with raiation at this frequency, the water molecules within the foo start to vibrate. The energy of the water molecules is then transferre to the rest of the foo, heating it up.