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									                                                        C.K.Cheung




                                 Optical Instrument




                h
                                                   

                                                   D




              h’

                                    h              ’




                                         ''
                                               '

          Angular magnification =
                                         

                                     h'
                                   = D
                                     h
                                     D

                                        h'
                                   =
                                        h


Note:

1. Far point =  for normal eye


2. D = least distance of distinct vision ~ 25 cm




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                                                                   C.K.Cheung




Compound Microscope
1. For normal adjustment, final image is formed at D.
2. Final image is virtual & inverted


                                   D
                                                             Eyepiece
                     Objective

                                 Fo           Fe

            Object                                      ’




    Final Image




h
                                      


                                          D




                        ' ' h" / D h" h" h'
                             '

Magnifying Power = m =      =         x  me xmo
                             h/ D   h h' h




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                                                                              C.K.Cheung


Eye-ring


                                                              Eyepiece
                     Objective
           Object

                                                         ’




                                                                         Eye-ring




1.   Eye-ring: the best position of the eye where it will receive as much light as possible
     from the object.
2.   Position of eye-ring: image position of objective lens formed by eyepiece.




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                                                                              C.K.Cheung



                                         Telescope:
 1/ Astronomical telescope

        For normal adjustment, the final image is formed at  . The final image is virtual
         and inverted.
        Length of telescope = fo+ fe


                                 fo                       fe




     
                                                h    ’




Construction Line




               ''
                   '
                     h / fe   f
           m=      =         o
                    h / fo   fe




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                                                                              C.K.Cheung


2/ Galilean telescope

1. For normal adjustment, the final image is at  . The final image is erect (an
    advantage)
2. The Galilean telescope is shorter than astronomical telescope
3. The eye-ring is situated between the 2 lenses, the eye should be as close as possible to
    the eyepiece, and the angle of view is rather limited when compared to astronomical
    telescope.( disadvantage )
4. Length of telescope = fo-fe
                             fo
                                                 fe
                         Construction
                         line




                                     ’
        
                                                          h




                 ''
                     '
                       h / fe   f
             m=      =         o
                      h / fo   fe




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                                                                                     C.K.Cheung



       Optical spectrometer




Slit



                                                                telescope
           collimator
                                                                                    Cross-wire

       When in use, the telescope must be adjusted so that parallel light rays entering the
       objective are brought to a focus at the cross-wires.
                                                                             m=2



                                                                                    m=1


                                                                                    m=0


                                                                                    m=1


                                                                                   m=2
                                      Diffraction grating


       Steps to be followed before an experiment:

       1. View a distant object through the telescope and adjust the image formed on the
            cross-wires can be seen clearly through the eyepiece.
       2. Align the telescope with the collimator. Look at the illuminated slit through the
            telescope. Adjust the distance of the slit from the collimator lens until the edges of
            the slit are sharp.
       3. level the turntable by adjusting the three screws underneath.




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                                                                                  C.K.Cheung


94’IIB

2. (a)
                                                                      eyepiece

                            objective lens
              object
                            P
             ho                 Q

                       Fo                Fo                FE                             FE
       hi

        final
        image



                                              Figure 2.1


            A student uses two converging lenses to set up a compound microscope in normal
            adjustment. Figure 2.1 shows two light rays, P and Q, form the top of an object
            falling on the objective lens of the microscope. The foci of the objective lens are
            denoted by FO and the foci of the eyepiece are denoted by FE.

            (i)   On Figure 2.1, complete the ray paths for P and Q as they pass through the
                  microscope, showing how the final image is formed.           (2 marks)

                                                                    eyepiece

                        objective lens
         object
                        P
        ho                  Q

                  Fo                Fo                 FE                           FE
  hi

   final
   image



                                          Figure 2.1


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                                                                          C.K.Cheung




   (ii)   Indicate on Figure 2.1 the visual angle  subtended by the final image at the
          eye of an observer using the microscope.                         (1 mark)

          Refer to diagram above

   (iii) Distinguish between linear magnification and angular magnification.
                                                                      (2 marks)
                                   length of image
         Linear Magnification =
                                   length of object

                                          visual angle of image
          Angular Magnification =
                                       visual angle of object at D


   (iv) Find the angular magnification of the microscope in terms of the height of
        the object, ho, and the height of the final image, hi. Show your working.
        (Take the least distance of distinct vision to be D)         (2 marks)

                                       h0
          Without microscope,  =
                                       D
                                  h1
          With microscope,  =
                                  D
                                          h
          Angular magnification =        = 1
                                          h0

(b) Figure 2.2 shows four light rays from an object passing through a microscope in
    normal adjustment. R and S come from the top of the object, T and U come from
    the bottom. R and T pass through the top of the objective lens, S and U pass
    through the bottom.

                     R
                 T
     object              S

                 U
                     objective                                       X
                       lens                       eyepiece



                                  Figure 2.2
   (i)    On Figure 2.2, X is the best position for the eye to view the image. With
          reference to the ray diagram, briefly explain the advantage(s) of choosing X
          as the viewing position.                                        (3 marks)


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                                                                  C.K.Cheung


          All the light from the objective lens ( or the object ) would pass
           through X.
          The image is then brightest
          The field of view is greatest.

(ii)   Why should the diameter of the beam            at   X be no wider than
       about 2 mm?                                               (1 mark)

       Matching the width of the beam to the diameter of the pupil.




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                                                                             C.K.Cheung




Revision on wave
81’
10.
                                                  15 cm




                                object




   A converging lens of focal length 15 cm is used as a magnifying glass with the final
   image at infinity. If the least distance of distinct vision is 25 cm, the angular
   magnification achieved is
                                              h / 15
   A.     0                              M=           5/3  C
   B.     1                                   h / 25
   C.     5/3
   D.     15
   E.     infinite
82’
15. A near-sighted person’s greatest distance of distinct vision is 0.9 m. His sight is
    improved by wearing spectacles which increase his greatest distance of distinct vision
    to 18 m. What is the magnitude of the focal length of the spectacle lenses?
    A.     0.86 m.
    B.     0.90 m.
    C.     0.95 m.                                                              F>v
    D.     17.1 m.                                                              C
    E.     18.9 m.                                              F
84’
15. Newton’s rings produced when a biconvex lens rests on a plane glass plate are
    observed using a travelling microscope. If the biconvex lens is very slowly moved
    vertically upwards from the lower glass plate, which of the following would be
    observed?

   A.   The central spot remains dark all the time.
   B.   The rings disappear immediately.
   C.   The rings move towards the centre.
   D.   The rings move out from the centre.
                                                                                C
   E.   The rings are no longer concentric.




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                                                                                              C.K.Cheung




16. Young’s slits are used to produce interference fringes with light of wavelength 600
    nm. A thin sheet of mica of refractive index 1.6 is placed in front of one of the slits
    and the centre of the fringe-system is displaced through 8 fringe widths. The
    thickness of the mica is

      A. 120 nm.                t ( n – 1) = 8 
      B.3 000 nm.               E
      C.4 000 nm.
      D.7 700 nm.
      E.8 000 nm.
85’
16. Two signal generators are connected to display the formation of beats on a C.R.O. screen. For one
    particular setting of the two signal generators, the following pattern is observed on the C.R.O.:




                                                         2.5 cm
      If the C.R.O. time base is set at 0.2 ms/cm, the beat frequency is
      A. 100 Hz.
      B. 200 Hz.
      C. 400 Hz.
      D. 1 000 Hz.
      E. 2 000 Hz.
17.
                                                    normal

                                                                  air

                                                                  water


                                                   ultra-sound
                                                     beam

    A beam of ultrasound is being emitted from a submarine under water towards the water surface.
    Which of the following statements is true?
    A. The refracted beam leaving the surface will bend away from the normal.
    B. The refracted beam will bend towards the normal.
    C. The refracted beam will travel in the same direction as the incident beam.
    D. Total internal reflection will occur.                                                      B
    E. The refracted beam will travel along the water surface.
18. The surface of a material of refractive index 1.8 is coated with a thin film of liquid of refractive index
    1.5 and thickness 200 nm. White light falls normally on the thin film. Which of the following light
    wavelengths (in air) is not reflected from the thin film?
    A.     400 nm
    B.     450 nm
    C.     600 nm
    D.     750 nm
    E.     800 nm                                                                           A




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                                                                                              C.K.Cheung



19. The image of a distant star produced by an astronomical telescope is a diffraction pattern. If the
    effective diameter of the objective lens is reduced by one-half by covering its outer parts with a stop,
    the area of the central maximum of the diffraction pattern is
    A.      decreased by a factor of 4.
    B.      halved.
    C.      unchanged.
    D.      doubled.
    E.      increased by a factor of 4.
20. When parallel light is incident at the Brewster angle in air on the surface of a glass block,
    A.      the light is totally reflected.
    B.      the reflected light is partially polarised.
    C.      the transmitted light is unpolarised.
    D. the reflected and refracted wavefronts are at right angles to each other.
     E.     the angle of incidence is equal to the angle of refraction.
87’
24.
                                                                           A

                                 S            M
                                                                           O


                                                                           B
      A plane mirror M is illuminated by monochromatic light from a slit S. The virtual image of S by
      reflection and S itself act as 2 coherent sources and the interference pattern is observed on the screen
      AOB at a distance from the mirror. Which of the following statements about the interference pattern
      on the screen is/are correct?
      (1) No interference pattern can be seen in the region OB on the screen.  x
      (2) As the mirror M moves downward, the separation of the fringes decreases.  x as d decreases
        (3) As the mirror M moves horizontally away from the screen, the separation of the fringes
                                                                                         decreases
      increases. correct, as d decreases
      A.      (1), (2) and (3)
      B.      (1) and (2) only
      C.      (2) and (3) only
      D.      (1) only
       E.     (3) only                                                                            E
88’
26.
                                     displacement


                                               a      2a      3a       x
                                     0



      The figure above shows the variation of the displacement of air molecules along the x-axis in a
      standing sound wave at a particular time. At what positions will the pressure remain constant with
      respect to time?
      A.      x = 0 and x = 2a only
      B.      x = a and x = 3a only
      C.      x = 0 and x = a only
      D.      x = 2a and x = 3a only                                                        B
      E.      x = 0, x = a, x = 2a and x = 3a


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                                                                                           C.K.Cheung




89’
21. The coated lens of a camera appears purple in daylight. According to the manufacturers, the coating
    has a refractive index of 1.25 and the material of the lens has a refractive index of 1.50. If the
    wavelength of yellow light in air is 520 nm, the approximate thickness of the coating is
    A.       104 nm.
    B.       130 nm.
    C.       180 nm.                                                                             A
    D.       210 nm.
    E.       260 nm.
22. Light of wavelength  is incident normally on a diffraction grating with p lines per millimetre. the
    second-order diffraction maximum is at an angle  from the central position. For a second grating
    with 3 p lines per millimetre illuminated normally by light of wavelength 5 /4, the angle between the
    first-order diffraction maximum and the central position is . Which of the following relations is
    correct ?
    A.       sin  = (5 sin )/12
    B.       sin  = sin (5 /12)
    C.       sin  = sin (15 /4)                                                                D
    D.       sin  = (15 sin )/8
    E.       sin  = sin (15 /8)
23. If the threshold of hearing is 10-12 W/m², a sound level of one microwatt per m² is above threshold by
    A.       6 dB.
    B.       11 dB.
    C.       60 dB.
    D.       110 dB.
    E.       120 dB.
24. A stationary radar source emits waves of frequency f, and wavelength  which are reflected from an
    object moving towards the source at a speed u. The reflected waves reaching a receiver standing near
    to the radar source will have an apparent wavelength of
    A.        - 2u/f.
    B.        - u/f.
    C.       .
    D.        + u/f.
      E.      + 2u/f.
90’
16.
                                                        V
                                                 deep
                                             P                  IV
                                   shallow

                                                                         III
                                                                         II
                                                                     I
                                                                Q
      The figure shows wave crests moving in the direction of the arrow towards the interface PQ between a
      shallow region and a deep region as shown in the figure above. Which of the lines shown may
      represent one of the wave crests in the deep region?
      A.     I
      B.     II
      C.     III
      D.     IV
      E.     V




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                                                                                              C.K.Cheung



17.




    A disc with a spot on it rotates at a constant speed in a darkened room. A students shines a
    stroboscopic lamp on it. When the flashing rate is 8 flashes per second, the disc appears stationary
    with two spots on it as shown. When the flashing rate is reduced to 2 flashes per second, the disc
    would appear to be stationary with
    A.       no spot.
    B.       one spot.
    C.       two spots.
    D.       four spots.
    E.       eight spots.
18. Which of the following represent the approximate noise levels
    (i) in a quiet school library?
    (ii) near the airport when an aircraft is taking off and flying overhead?
         (i)          (ii)
    A.       30 dB            60 dB
    B.       60 dB            90 dB
       C. 30 dB                90 dB
    D.      90 dB             60 dB
    E.      60 dB             30 dB
19. The intensity of a sound wave is proportional to the square of the amplitude of the wave. If two
    waves of the same frequency are superimposed in phase, the total intensity is proportional to
    A. the mean value of the intensities of the two waves.
    B. the square of the sum of the two amplitudes.
    C. the square of the mean value of the two amplitudes.
    D. the square of the difference of the two amplitudes.
    E. the sum of the intensities of the two waves.
20. In a simple astronomical telescope, under normal adjustment, which of the following statements is/are
    correct?
    (1) The first image is formed at the focal plane of the objective.
    (2) The first image is real and inverted.
    (3) The focal length of the objective is longer than that of the eyepiece.
    A.      (1), (2) and (3)
    B.      (1) and (2) only
    C.      (2) and (3) only
    D.      (1) only
    E.      (3) only
21.
                                                      o
                                                 30



      A boat travels in shallow water, in which waves of all wavelengths travel at a speed of 4.0 m/s.   What
      is the speed of the boat if the bow wave generated by the boat has an apex angle of 30º?
      A.      2.0 m/s
      B.      2.3 m/s
      C.      4.0 m/s
      D.      6.9 m/s
      E.     8.0 m/s



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                                                                                              C.K.Cheung


22.




      The figure shows two pulses travelling to the right along a rope. The right-hand end of the rope is
      fixed to a wall. The following figures represent predicted positions of the pulses at later times (where
      appropriate, the arrows indicate the direction of a pulse). Which of the following could NOT arise
      from the initial given condition?
      (1)




      (2)




      (3)




      A.     (1), (2) and (3)
      B.     (1) and (2) only
      C.     (2) and (3) only
      D.     (1) only
      E.     (3) only

23.
                                                                          A
                                              L1


                                  G



                                              L2
                                                                          B

      2 loudspeakers L1 and L2 are connected to a signal generator G. A microphone is moved along the
      line AB and the variation in intensity is noted. Which of the following statements concerning the
      above arrangement is/are correct?

      (1) If the separation of the 2 loudspeakers is less than the wavelength of the sound emitted, no
          alternation of maxima and minima can be detected along AB.
      (2) If the frequency of the sound waves emitted is increased, the separation between adjacent maxima
          along AB will be increased.
      (3) If the 2 loudspeakers are vibrating in antiphase, no alternation of maxima and minima will be
          detected along AB.




                                                                                                           15
                                                                                                C.K.Cheung



    A.      (1), (2) and (3)
    B.      (1) and (2) only
    C.      (2) and (3) only
    D.      (1) only
    E.      (3) only




24. Sound waves of frequency f are emitted by a source S. When S is moved with speed u (relative to the
    ground) towards a stationary observer O, a rise in pitch of f is detected. Which of the following
    statements is/are correct?

    (1) The speed of sound waves relative to the observer is unaffected by the motion of S.
    (2) If both S and O move in the same direction with speed u, no rise in pitch will be detected.
    (3) If S is at rest with O moving towards it at speed u, the rise in pitch will also be f.

    A.      (1), (2) and (3)
    B.      (1) and (2) only
    C.      (2) and (3) only
    D.      (1) only
    E.      (3) only


25. When parallel light is incident at the Brewster angle in air on the surface of a glass block, which of the
    following statements is/are correct?

    (1)   The refracted light is plane-polarised.
    (2)   The reflected light is plane-polarised.
    (3) The reflected ray and the refracted ray are at right angles to each other.

    A.      (1), (2) and (3)
    B.      (1) and (2) only
    C.      (2) and (3) only
    D.      (1) only
    E.      (3) only


26. White light diffracted by a single slit falls on a white screen.   Which of the following statements is/are
    correct?

    (1) The centre of the diffraction pattern is white.
    (2) The first minimum is closer to the centre for red light than for blue light.
    (3) The central band width is increased as the slit width is increased.

    A.      (1), (2) and (3)
    B.      (1) and (2) only
    C.      (2) and (3) only
    D.      (1) only
    E.      (3) only




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