AH Division of Wavefront and Amplitude Answers

Transcription

1 AH Division of Wavefront and Amplitude Answers 1. Interference. 2. a) Splitting a single light beam into two beams, a reflected beam and a transmitted beam, at a surface between two media of two different refractive index. b) More than two beams could be produced. 3. a) Sources with the same frequency i.e a constant phase difference. b) Two overlapping beams from the same single source. c) They will not have a constant phase relationship. d) Two loudspeakers connected to the same signal generator, emitting the same frequency of sound will produce an interference pattern. 4. a) (S2Q - S1Q) = mλ b) (S2Q - S1Q) = (m + 1/2)λ 5. a) Optical Path Length = n x Geometrical Path Length. b) Optical Path Length is the length of the path in the medium involved. Geometrical Path Length is the length of the path in air. c) For the ray of light passing through the medium of refractive index 1.45 it will have a wavelength of 1.45 times smaller than that in air. It will have 1.45 times the no. of waves in the medium compared to air. 6. a) The difference in two optical path lengths. b) Phase difference = 2π/λ x Optical Path Length. c) If the optical path difference is a whole number of waves then the phase difference is a multiple of 2π. 7. a) A reflected pulse goes back from the metal gate end of the rope back to the person holding the rope. b) 180 or π rad.

2 8. a) No phase change. b) 180 or π rad. 9. a) The amplitude of the beam is divided by reflection and transmission at the boundary of the two mediums. b) Reflected rays have a different path difference and will interfere when brought together. This also happens with transmitted rays at the other side. c) 2nt = mλ n = refractive index of the medium t = thickness of the medium m = order of the fringes λ = wavelength of the light used. 10. a) Δx = λ/(2tanθ) and Δx = λl/2d. b) To cut down the percentage uncertainty in Δx to provide a more accurate answer for Δx. 11. a) Two glass slides with a sheet of the paper placed at one end to form a wedge. A light source of known wavelength is shone down from above the top slide. b) Δx = λl/2d => D = λl/2δx D = (600x10-9 x 80x10-3 )/(2x1.4x10-3 ) = 1.71x10-5 m. 12. a) The reflected light has no green/yellow present. b) A thin coating of magnesium fluoride on the surface of the lens. c) 1 < n < nglass. d) For cancellation of reflected light Optical Path difference = λ/2 Optical Path length in fluoride = 2nd 2nd = λ/2 d = λ/4n.

3 13. a) Division of Wavefront. b) Δx = λd/d Δx = Fringe separation (m) λ = Wavelength of light used (m) D = Distance from slits to the screen (m) d = Distance between the slits (m). 14. a) Division of Amplitude. b) c) i) Fringes become closer together. ii) Fringe separation Δx α λ. => λ water < λ air. OR Optical path difference increases by a factor of n. OR Consecutive maxima and minima happen sooner.

4 15. a) i) ii) t = λ/4n = 500x10-9 /(4 x 1.38) = 9.1x10-8 m. iii) 500nm is around the middle of the visible spectrum and so red and blue light is reflected. They combine to give purple. b) Fringe spacing = 0.1/4 = 0.025m. 16. a) i) Constant phase relationship between the sources. ii) Optical path difference = path difference x n. iii) A) Optical path difference = (m + ½)λ. B) Optical path difference = mλ. iv) There will be a phase change of π at the lower surface of the slide. b) i) Rays reflected from the surface of MgF interfere destructively with rays reflected from the glass surface. ii) d = λ/4n = 550x10-9 /(4 x1.38) = 9.96x10-8 m.

5 17. a) i) iii) An uncertainty should be quoted to one significant figure. b) c) i) The % uncertainty in x is very small compared to the percentage uncertainty in d. ii) The slit separation d.

6 18. a) i) ii) d = (589x10-9 x 0.075) / (2 x 3.4x10-4 ) = 6.5x10-5 m. b) i) d = λ/4n = 548x10-9 /(4 x1.38) = 9.9x10-8 m. ii) n MgF < n Liquid. => No phase change at the surface => Constructive Interference => More light reflected. c) Path length in oil depends on the angle of incidence or thickness. => Different colours are seen due to interference. 19. a) i) A) π. B) π. ii) Reflected rays interfere destructively if optical path difference = λ/2. iii) So more light is transmitted through the lens to produce a brighter image. iv) b) Fringe separation, length of glass plates and the wavelength of sodium light. Δx = λl/2d.

7 20. a) Division of Wavefront. b) c) i) Increase Δx. Smaller % uncertainty in d or Δx. ii) Fainter fringes or broader fringes or not all fringes are seen as the screen is not big enough.

8 21. a) i) ii) iii) b) i) ii) iii)

9 22. a) b) c) d) i) ii) iii)