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(d)Calculate the refractive index of the liquid.answer (2)(Total 8 marks)18For a plane transmission diffraction grating, the diffraction grating equation for the first orderbeam is:λ d sin θ(a)The figure below shows two of the slits in the grating. Label the figure below with thedistances d and λ.(2)(b)State and explain what happens to the value of angle θ for the first order beam if thewavelength of the monochromatic light decreases.(2)St Bede's Catholic Comprehensive School and Byron CollegePage 21 of 83

(c)A diffraction grating was used with a spectrometer to obtain the line spectrum of star Xshown in the figure below. Shown are some line spectra for six elements that have beenobtained in the laboratory.Place ticks in the boxes next to the three elements that are present in the atmosphere ofstar X.(2)(d)The diffraction grating used to obtain the spectrum of star X had 300 slits per mm.(i)Calculate the distance between the centres of two adjacent slits on this grating.answer m(1)(ii)Calculate the first order angle of diffraction of line P in the figure above.answer degrees(2)(Total 9 marks)St Bede's Catholic Comprehensive School and Byron CollegePage 22 of 83

19A single slit diffraction pattern is produced on a screen using a laser. The intensity of the centralmaximum is plotted on the axes in the figure below.(a)On the figure above, sketch how the intensity varies across the screen to the right of thecentral maximum.(2)(b)A laser is a source of monochromatic, coherent light. State what is meant bymonochromatic lightcoherent light(2)(c)Describe how the pattern would change if light of a longer wavelength was used.(1)(d)State two ways in which the appearance of the fringes would change if the slit was madenarrower.(2)St Bede's Catholic Comprehensive School and Byron CollegePage 23 of 83

(e)The laser is replaced with a lamp that produces a narrow beam of white light. Sketch andlabel the appearance of the fringes as you would see them on a screen.(3)(Total 10 marks)20The figure below shows a cross-section through an optical fibre.(a)Explain the purpose of part X.(1)St Bede's Catholic Comprehensive School and Byron CollegePage 24 of 83

(b)The critical angle for the optical fibre is to be 60 and the absolute refractive index for theglass in the core of the fibre is 1.6.Calculate the required absolute refractive index for part Y.absolute refractive index for part Y(3)(c)Explain why dispersion occurs in an optical fibre.(2)(Total 6 marks)St Bede's Catholic Comprehensive School and Byron CollegePage 25 of 83

21Figure 1 shows a cross-section through an optical fibre used for communications.Figure 1(a)(i)Name the part of the fibre labelled X.(1)(ii)Calculate the critical angle for the boundary between the core and X.answer degrees(2)St Bede's Catholic Comprehensive School and Byron CollegePage 26 of 83

(b)(i)The ray leaves the core at Y. At this point the fibre has been bent through an angle of30 as shown in Figure 1.Calculate the value of the angle i.answer degrees(1)(ii)Calculate the angle r.answer degrees(2)St Bede's Catholic Comprehensive School and Byron CollegePage 27 of 83

(c)The core of another fibre is made with a smaller diameter than the first, as shown in Figure2. The curvature is the same and the path of a ray of light is shown.Figure 2(c)State and explain one advantage associated with a smaller diameter core.(2)(Total 8 marks)St Bede's Catholic Comprehensive School and Byron CollegePage 28 of 83

22(a)The speed of light is given byc fλState how each of these quantities will change, if at all, when light travels from air to glass.cfλ(3)Figure 1 shows a side view of a step index optical fibre.Figure 1(b)Ray A enters the end of the fibre and then undergoes total internal reflection.On Figure 1 complete the path of this ray along the fibre.(2)(c)(i)The speed of light in the core is 2.04 108 ms–1. Show that the refractive index of thecore is 1.47.(2)(ii)Show that the critical angle at the boundary between the core and the cladding isabout 80 .refractive index of the cladding 1.45(2)St Bede's Catholic Comprehensive School and Byron CollegePage 29 of 83

(d)Ray B enters the end of the fibre and refracts along the core-cladding boundary. Calculatethe angle of incidence, θ, of this ray at the point of entry to the fibre.answer degrees(3)(e)Figure 2 shows a pulse of monochromatic light (labelled X) that is transmitted a significantdistance along the fibre. The shape of the pulse after travelling along the fibre is labelled Y.Explain why the pulse at Y has a lower amplitude and is longer than it is at X.Figure 2(2)(Total 14 marks)St Bede's Catholic Comprehensive School and Byron CollegePage 30 of 83

23The diagram below shows a section of a typical glass step-index optical fibre used forcommunications.(a)Show that the refractive index of the core is 1.47.(1)(b)The refracted ray meets the core-cladding boundary at an angle exactly equal to the criticalangle.(i)Complete the diagram above to show what happens to the ray after it strikes theboundary at X.(2)(ii)Calculate the critical angle.critical angle degrees(1)(iii)Calculate the refractive index of the cladding.refractive index (2)St Bede's Catholic Comprehensive School and Byron CollegePage 31 of 83

(c)Give two reasons why optical fibres used for communications have a cladding.reason 1reason 2(2)(Total 8 marks)24The figure below shows a glass prism. Light is directed into the prism at an angle of 56 .The path of the ray of light is shown as is it enters the prism.(a)(i)Calculate the refractive index of the glass.answer (2)(ii)Calculate the critical angle for the glass-air boundary.answer degrees(2)St Bede's Catholic Comprehensive School and Byron CollegePage 32 of 83

(b)On the figure above, continue the path of the ray of light until it emerges from the prism.(2)(Total 6 marks)25The diagram below shows three transparent glass blocks A, B and C joined together. Each glassblock has a different refractive index.(a)State the two conditions necessary for a light ray to undergo total internal reflection at theboundary between two transparent media.condition 1condition 2(2)St Bede's Catholic Comprehensive School and Byron CollegePage 33 of 83

(b)Calculate the speed of light in glass A.refractive index of glass A 1.80speed of light ms 1(2)(c)Show that angle θ is about 30o.(2)(d)The refractive index of glass C is 1.40.Calculate the critical angle between glass A and glass C.critical angle degrees(2)(e)(i)State and explain what happens to the light ray when it reaches the boundarybetween glass A and glass C.(2)(ii)On the diagram above continue the path of the light ray after it strikes the boundarybetween glass A and glass C.(1)(Total 11 marks)St Bede's Catholic Comprehensive School and Byron CollegePage 34 of 83

26The figure below shows a spectrometer that uses a diffraction grating to split a beam of light intoits constituent wavelengths and enables the angles of the diffracted beams to be measured.(a)Give one possible application of the spectrometer and diffraction grating used in this way.(1)(b)(i)When the spectrometer telescope is rotated from an initial angle of zero degrees, aspectrum is not observed until the angle of diffraction θ is about 50 . State the orderof this spectrum.(1)(ii)White light is directed into the spectrometer. Light emerges at A and B. State onedifference between the light emerging at B compared to that emerging at A.(1)St Bede's Catholic Comprehensive School and Byron CollegePage 35 of 83

(c)The angle of diffraction θ at the centre of the observed beam B in the image above is 51.0 and the grating has 1480 lines per mm.Calculate the wavelength of the light observed at the centre of beam B.wavelength m(3)(d)Determine by calculation whether any more orders could be observed at the wavelengthcalculated in part (c).(2)(Total 8 marks)27(a)A laser emits monochromatic light.Explain the meaning of the term monochromatic light.(1)St Bede's Catholic Comprehensive School and Byron CollegePage 36 of 83

(b)The diagram below shows a laser emitting blue light directed at a single slit, where the slitwidth is greater than the wavelength of the light. The intensity graph for the diffracted bluelight is shown.The laser is replaced by a laser emitting red light.On the axes shown in the diagram above sketch the intensity graph for a laser emitting redlight.(2)(c)State and explain one precaution that should be taken when using laser light(2)St Bede's Catholic Comprehensive School and Byron CollegePage 37 of 83

(d)The red laser light is replaced by a non-laser source emitting white light.Describe how the appearance of the pattern would change.(3)(Total 8 marks)28Figure 1 shows a ray of light A incident at an angle of 60 to the surface of a layer of oil that isfloating on water.refractive index of oil 1.47refractive index of water 1.33Figure 1(a)(i)Calculate the angle of refraction θ in Figure 1.angle degrees(2)St Bede's Catholic Comprehensive School and Byron CollegePage 38 of 83

(ii)Calculate the critical angle for a ray of light travelling from oil to water.angle degrees(2)(iii)On Figure 1 continue the path of the ray of light A immediately after it strikes theboundary between the oil and the water.(2)(b)In Figure 2 a student has incorrectly drawn a ray of light B entering the glass and thenentering the water before totally internally reflecting from the water–oil boundary.Figure 2The refractive index of the glass is 1.52 and the critical angle for the glass–water boundaryis about 60 .St Bede's Catholic Comprehensive School and Byron CollegePage 39 of 83

Give two reasons why the ray of light B would not behave in this way. Explain youranswers.reason 1explanationreason 2explanation(4)(Total 10 marks)29The diagram shows Young’s double-slit experiment performed with a tungsten filament lamp asthe light source.(a)On the axes in the diagram above, sketch a graph to show how the intensity varies withposition for a monochromatic light source.(2)St Bede's Catholic Comprehensive School and Byron CollegePage 40 of 83

(b)(i)For an interference pattern to be observed the light has to be emitted by twocoherent sources.Explain what is meant by coherent sources.(1)(ii)Explain how the use of the single slit in the arrangement above makes the light fromthe two slits sufficiently coherent for fringes to be observed.(1)(iii)In this experiment light behaves as a wave.Explain how the bright fringes are formed.(3)St Bede's Catholic Comprehensive School and Byron CollegePage 41 of 83

(c)(i)A scientist carries out the Young double-slit experiment using a laser that emits violetlight of wavelength 405 nm. The separation of the slits is 5.00 10–5 m.Using a metre ruler the scientist measures the separation of two adjacent brightfringes in the central region of the pattern to be 4 mm.Calculate the distance between the double slits and the screen.distance m(2)(ii)Describe the change to the pattern seen on the screen when the violet laser isreplaced by a green laser. Assume the brightness of the central maximum is thesame for both lasers.(1)(iii)The scientist uses the same apparatus to measure the wavelength of visibleelectromagnetic radiation emitted by another laser.Describe how he should change the way the apparatus is arranged and used in orderto obtain an accurate value for the wavelength.(3)(Total 13 marks)St Bede's Catholic Comprehensive School and Byron CollegePage 42 of 83

30An optical fibre consists of a core, cladding and an outer sheath.(a)State the purpose of the outer sheath in an optical fibre.(1)(b)For one fibre, the speed of monochromatic light in the core is 1.97 108 m s 1 and thespeed in the cladding is 2.03 108 m s 1.Calculate the critical angle for this light at the interface between the core and the cladding.critical angle degrees(2)(Total 3 marks)31Diamond jewels sparkle because light that enters the diamond at different incident angles isreflected back to an observer. Figure 1 shows the path of one of these incident rays through adiamond.Figure 1St Bede's Catholic Comprehensive School and Byron CollegePage 43 of 83

(a)(i)Calculate the critical angle for diamond.Refractive index of diamond 2.42critical angle degree(2)(ii)The ray shown in Figure 1 enters at an angle of incidence of 50.2 .Calculate the angle of refraction θ.θ degree(2)(iii)The angles of a diamond are chosen to maximise the amount of light reflected.Figure 2 shows a diamond with different angles to that of a normally shapeddiamond. The dotted lines show the normal shape of a diamond.Figure 2Draw on Figure 2 the path of the ray until it leaves the diamond.(2)St Bede's Catholic Comprehensive School and Byron CollegePage 44 of 83

(iv)Moissanite is a transparent material with a refractive index of 2.67.Discuss whether this material, if made to the diamond shape shown in Figure 1,would reflect light back more or less than diamond.(2)(b)Figure 3 shows an infrared ray entering an optical fibre. The refractive index of the core is1.55 at infrared frequencies.Figure 3(i)Calculate the speed at which infrared radiation travels in the core.speed m s 1(1)St Bede's Catholic Comprehensive School and Byron CollegePage 45 of 83

(ii)The wavelength of this infrared radiation is 1300 nm in air.Calculate the wavelength of infrared in the core.wavelength m(2)(iii)State one reason for surrounding the core with cladding.(1)(Total 12 marks)32(a)Tick ( ) the appropriate boxes in the table to indicate how the wavelength, frequency andspeed of light are affected when a ray of light travels from air into glass.WavelengthFrequencySpeedincreasesstays the samedecreases(2)St Bede's Catholic Comprehensive School and Byron CollegePage 46 of 83

(b)Figure 1 shows a right-angled glass prism in contact with a transparent substance on oneof the faces. One of the other angles of the prism is θ.Figure 1(i)A ray A enters perpendicularly to one face of the prism. It is partially refracted andpartially reflected at the interface between the glass and the transparent substance.The angle of refraction is 65.0 . The ray eventually leaves at an angle α to thesurface of the transparent substance.Determine the angle α.angle α degree(2)(ii)Determine the angle θ in Figure 1.angle θ degree(2)St Bede's Catholic Comprehensive School and Byron CollegePage 47 of 83

(c)Figure 2 shows another ray entering the prism.Figure 2(i)Identify the effect that takes place at X in Figure 2.(1)(ii)Explain, with a diagram, how the effect that occurs at X is used to transmitinformation along an optic fibre.(3)(Total 10 marks)St Bede's Catholic Comprehensive School and Byron CollegePage 48 of 83

33Musicians can use tuning forks to tune their instruments.A tuning fork produces a specific frequency when it vibrates.Figure 1 shows a tuning fork vibrating in air at a single instant in time.The circles represent the positions of air particles in the sound wave.Figure 1(a)The tuning fork emits a wave that has a frequency of 0.51 kHz.(i)State the meaning of the term frequency of a wave.(1)(ii)Air particles vibrate in different phases in the direction in which the wave is travelling.Calculate the minimum separation of particles that vibrate 180 out of phase.speed of sound in air 340 m s–1minimum separation m(3)St Bede's Catholic Comprehensive School and Byron CollegePage 49 of 83

(b)A student sets a tuning fork of lower frequency vibrating at the same time as the 0.51 kHztuning fork in part (a).The student detects the resultant sound wave with a microphone. The variation with time ofthe voltage generated by the microphone is shown in Figure 2.Figure 2(i)Explain why the two tuning forks are not coherent sources of sound waves.(2)(ii)Explain why the resultant sound has a minimum amplitude at 50 ms.(3)St Bede's Catholic Comprehensive School and Byron CollegePage 50 of 83

(iii)Calculate the frequency of the tuning fork that emits the lower frequency.frequency Hz(3)(c)A signal generator connected to a loudspeaker produces a sinusoidal sound wave with afrequency of 440 Hz.The variation in air pressure with time for this sound is shown in Figure 3.Figure 3A violin string has a fundamental frequency (first harmonic) of 440 Hz.Figure 4 shows the variation in air pressure with time for the sound created by the violinstring.Figure 4St Bede's Catholic Comprehensive School and Byron CollegePage 51 of 83

(i)The two sounds have the same pitch but sound different.What term describes the difference between the sounds heard?Tick ( ) the correct answer.Frequency modulationOctavesPath differenceQuality(1)(ii)The complex sound in Figure 4 can be electronically synthesised.Describe the process of electronically synthesising this sound.(3)(Total 16 marks)St Bede's Catholic Comprehensive School and Byron CollegePage 52 of 83

34The diagram below shows the paths of microwaves from two narrow slits, acting as coherentsources, through a vacuum to a detector.(a)Explain what is meant by coherent sources.(2)(b)(i)The frequency of the microwaves is 9.4 GHz.Calculate the wavelength of the waves.wavelength m(2)St Bede's Catholic Comprehensive School and Byron CollegePage 53 of 83

(ii)Using the diagram above and your answer to part (b)(i), calculate the path differencebetween the two waves arriving at the detector.path difference m(1)(c)State and explain whether a maximum or minimum is detect

(b) The light source is replaced by a monochromatic light source of unknown wavelength. A narrow beam of light from this light source is directed normally at the grating. Measurement of the angle of diffraction of the second order beam gives a value of 42.1 . Calculate the wavelength of this light source.