(a) (i) Label the diagram of the human eye to show the lens, retina and optic nerve.

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1 Practice Test: 28 marks (42 minutes) Additional Problem: 37 marks (56 minutes) 1. This question is about the human eye. (a) (i) Label the diagram of the human eye to show the lens, retina and optic nerve. (1) (ii) Outline the function of the rods and the cones in the retina. (3) Outline what is meant by accommodation in the eye. (3) (Total 7 marks) 1/12

2 2. This question is about the Doppler effect. At one point in an artery, blood cells flow along the axis of the artery with speed v, as shown. A parallel beam of ultrasound of frequency 4.5 MHz is incident on the artery at an angle of 40. The speed of ultrasound in the body tissues is c = m s 1. The ultrasound detected after reflection from the blood cells is found to be Doppler-shifted in frequency by 740 Hz. The expression for the Doppler shift f of the ultrasound of frequency f may be assumed to be ( 2 fv cos ) f =. c (a) For this stated expression, explain the inclusion of (i) the factor of 2. (ii) the factor cos θ. (1) Determine a value for the speed of the blood cells in the artery. (Total 5 marks) 2/12

3 3. This question is about standing waves. A string is attached between two rigid supports and is made to vibrate at its fundamental frequency (first harmonic) f. The diagram shows the displacement of the string at t = 0. (a) Draw the displacement of the string at time (i) t = 1 4 f (1) (ii) t = 1 2 f (1) The distance between the supports is 1.0 m. A wave in the string travels at a speed of 240 m s 1. Calculate the frequency of the vibration of the string. (c) An organ pipe that is open at one end has the same fundamental frequency as the string in part. The speed of sound in air is 330 m s 1. Determine the length of the pipe. (Total 6 marks) 3/12

4 4. This question is about diffraction and resolution. (a) Light from a monochromatic point source S 1 is incident on a narrow rectangular slit. After passing through the slit, the light is incident on a screen some distance away from the slit. The graph shows how the intensity distribution on the screen varies with the angle θ shown in the diagram. (i) The width of the slit is m. Use data from the graph to calculate the wavelength of the light. 4/12

5 (ii) An identical source S 2 is placed close to S 1 as shown. The images of the two sources on the screen are just resolved according to the Rayleigh criterion. On the graph above, draw the intensity distribution of the second source. (1) The Very Large Array (VLA) is used to analyse radio signals from distant galaxies. The combined diameter of the VLA is 36 km. A region of linear size L inside the radio galaxy M87 emits radio waves with a frequency of 43 GHz. The galaxy is a distance m from Earth. The VLA can just resolve the radio emitting region. Estimate the value of L. (3) (Total 6 marks) 5/12

6 5. This question is about polarization. (a) A beam of unpolarized light of intensity I 0 is incident on a polarizer. The polarization axis of the polarizer is initially vertical as shown. The polarizer is then rotated by 180 in the direction shown. On the axes below, sketch a graph to show the variation with the rotation angle θ, of the transmitted light intensity I, as θ varies from 0 to 180. Label your sketch-graph with the letter U. The beam in (a) is now replaced with a polarized beam of light of the same intensity. The plane of polarization of the light is initially parallel to the polarization axis of the polarizer. The polarizer is then rotated by 180 in the direction shown. On the same axes in (a), sketch a graph to show the variation with the rotation angle θ, of the transmitted light intensity I, as θ varies from 0 to 180. Label your sketch-graph with the letter P. (Total 4 marks) 6/12

7 6. This question is about vision and resolution. (a) Compare scotopic with photopic vision. The graph shows the variation with wavelength λ of the sensitivity I, of the rod and the cone cells of a human eye. A red piece of paper and a blue piece of paper are both viewed in very low intensity light. Each piece of paper reflects the same intensity of light. With reference to the graph, state and explain which one of the two pieces of paper will be more clearly visible. (3) 7/12

8 (c) The diameter of the pupil of a human eye is 1.5 mm. (i) Calculate the minimum angular separation of two points that can be resolved by the human eye for light of wavelength 680 nm. (1) (ii) Two stars, the same distance from Earth, are separated by a distance of m. Both stars emit light of wavelength 680 nm. The two stars are just resolved by an observer on Earth. Estimate the distance to the two stars. (Total 8 marks) 7. This question is about the Doppler effect. The sound emitted by a car s horn has frequency f, as measured by the driver. An observer moves towards the stationary car at constant speed and measures the frequency of the sound to be f. (a) Explain, using a diagram, any difference between f and f. (3) 8/12

9 The frequency f is Hz. An observer moves towards the stationary car at a constant speed of 15.0 m s 1. Calculate the observed frequency f of the sound. The speed of sound in air is m s 1. (Total 5 marks) 8. This question is about the Doppler effect. The wavelength diagram shown represents three lines in the emission spectrum sample of calcium in a laboratory. A distant star is known to be moving directly away from the Earth at a speed of 0.1c. The light emitted from the star contains the emission spectra of calcium. On the diagram sketch the emission spectrum of the star as observed in the laboratory. Label the lines that correspond to A, B, and C with the letters A*, B*, and C*. Numerical values of the wavelengths are not required. (Total 3 marks) 9. This question is about the eye and resolution. A student measures the aperture of the iris of one of her eyes as 2.0 mm in sunlight and 7.0 mm in moonlight. The intensity at her eye of sunlight is 106 times greater than the intensity of moonlight. (a) (i) Determine the following ratio. power of light enteringtheeyein sunlight power of light enteringtheeyein moonlight (3) 9/12

10 (ii) Suggest why your answer in (a)(i) indicates that the change in diameter of the iris is not the principal mechanism by which the eye is able to adjust to different light intensities. (1) (i) State the Rayleigh criterion. (ii) Suggest, with reference to the Rayleigh criterion, whether the ability of the eye to resolve the image of two objects is greater in sunlight or in moonlight. (4) (c) Outline the different functions of the rods and the cones on the retina of the eye in their response to sunlight and to moonlight. Rods: Cones:... (4) (Total 14 marks) 10. This question is about polarization. (a) State what is meant by polarized light (1) 10/12

11 Polarized light of intensity I 0 is incident on an analyser. The transmission axis of the analyser makes an angle with the direction of the electric field of the light. (i) Calculate, in terms of I 0, the intensity of light transmitted through the analyser when = (1) (ii) On the axes below, sketch a graph to show the variation with angle of the intensity of the transmitted light. (c) Outline how polarizing sunglasses reduce glare from a reflecting surface (3) (Total 7 marks) 11. This question is about diffraction and resolution. (a) A parallel beam of monochromatic light is incident on a narrow rectangular slit. After passing through the slit, the light is incident on a distant screen. Point X is the midpoint of the slit. (i) On the axes below, sketch a graph to show how the intensity of the light on the screen varies with the angle θ shown in the diagram. 11/12

12 (3) (ii) The wavelength of the light is 520 nm, the width of the slit is 0.04 mm and the screen is 1.2 m from the slit. Show that the width of the central maximum of intensity on the screen is about 3 cm. Points P and Q are on the circumference of a planet as shown. By considering the two points, outline why diffraction limits the ability of an astronomical telescope to resolve the image of the planet as a disc. (3) (Total 8 marks) 12/12

13 Mark Scheme 1. (a) (i) Correct positioning of: lens, retina and optic nerve; 1 (ii) convert a light signal into an electrical signal; rods are used for black and white vision/contrast/scotopic; cones are used for colour vision/photopic; 3 for objects at different distances from the eye; for the image to be focused; the (ciliary) muscle changes the shape of the lens; 3 [7] 2. (a) (i) either observer sees image of blood cell; moving at twice speed of blood cell; or Doppler shift observed by blood cell; superposed on shift when cell acts as moving source; 2 Award [1] if mentioned that Doppler effect occurs twice. (ii) need component of velocity of cell along direction of ultrasound beam; v cos = v = 0.16 m s 1 ; Award [1] if the speed of light is used. 2 [5] 3. (a) (i) 1 (ii) 1 13/12

14 v f = ; to give f = 120Hz; (c) λ = 4L = 120 = 0.69m; 2 [6] 4. (a) (i) angle of first minimum is rad; thus λ = bθ = l0 4 = 5.6 l0 7 m; 2 (ii) as shown above; 1 Accept if second pattern is drawn to the left of the other wavelength is = m; telescope can resolve an angular separation of θ = ; 3 b 3610 and so L = Dθ = = m; 3 [6] 14/12

15 5. (a) horizontal line; (labelled U) through half the incident intensity; 2 curve starting at I 0 ; (labelled P) with minima and maxima as shown; 2 [4] 6. (a) Scotopic vision / uses rod cells/is used in low intensity light/does not distinguish between colours/does not see detail; Photopic vision / uses cone cells/is used in high intensity light/distinguishes colours/sees detail; 2 Scotopic vision using rods is to be used; sensitivity for blue wavelengths is high for rod cells; and so blue will be seen most clearly; Award [0] for bald answer, blue only, or incorrect argument. 3 (c) (i) θ = rad; 3 d Accept answer missing the factor of 1.22 i.e rad. Do not penalize absence of rad. 13 s (ii) d = ; d = m; 2 Accept answer that uses rounded answer from (i) i.e. d = m or has missed the factor of 1.22 i.e. d = m. [8] 15/12

16 7. (a) circular wavefronts around source, equally spaced; moving observer intercepts more wavefronts per unit time / the time between intercepting successive wavefronts is less; hence observes a higher frequency / f > f; or circular wavefronts around source, equally spaced; the velocity of the sound waves with respect to the observer is greater; v since f =, observed frequency is also greater; 3 v u f = f 300 ; v 330 = 314 Hz; Award [0] for use of moving source formula. Award [1] for use of v-u o to give 286 Hz. 2 [5] 8. The diagram should be as follows: lines shifted all in the same direction; shift in B or the shift in C being noticeably larger than the shift in A; lines shifted right; 3 Award [2 max] if lines are not labelled. [3] 9. (a) (i) power = area intensity; ratio = 10 6 ; 7.0 = ; 3 16/12

17 (ii) if iris were to be the principal 2 mechanism, then ratio would need to be about 2 or 7 ; 1 (i) for two images (of two objects) just to be distinguished/ to be seen as separate images; maximum of one diffraction pattern must lie on first minimum of second; 2 (1.22) (ii) images resolved when θ ; b where θ is angle subtended at eye by object and b is the diameter of the pupil; wavelength unchanged; larger diameter, better resolution; (accept vice versa) 4 (c) rods: scotopic vision / black and white vision; function best in low light intensity such as moonlight; cones: photopic vision / colour vision; function best in high light intensity such as sunlight; 4 Award [3 max] for omission of reference to moonlight and sunlight. [14] 10. (a) light where the direction of the (electric) field is always/predominantly in the same plane; 1 2 I 0 (i) I I 0 cos (ii) ; general cos 2 shape; max at = 0 and curve touches horizontal axis at = 90; 2 17/12

18 (c) light is (partially) horizontally polarized by reflection; sunglasses have a transmission axis at 90 to the plane of reflected light; intensity of reflected light is reduced; 3 Award full marks for a clearly labelled diagram. [7] 11. (a) (i) general correct shape touching axis and symmetric about θ = 0 (at least one secondary maxima on each side); (judge by eye) central maximum wider than secondary maxima; secondary maxima at most one third intensity of central maximum; 3 d D (ii) ; 2 b d = = m cm 2 Award [2 max] for a sensible argument. e.g. light from each point forms a diffraction pattern after being focussed by the eyepiece of the telescope; if the diffraction patterns are not sufficiently well separated then the points will not be resolved as separate sources; Award [1 max] for the conclusion. e.g. if the points cannot be resolved as separate sources the planet cannot be seen as a disc; 3 [8] [14] 18/12

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