## Saturday, 6 September 2014

### INTERFERENCE 1 PROBLEMS

INTERFERENCE 1

Where necessary take the velocity of light as = 3x108 ms-1 and the velocity of sound in air 330 ms-1
1. What conditions are necessary for a static interference pattern to occur?

2. (a) What is meant by coherent light?
(b) What is meant by interference?
(c) What is meant by path difference?
(d) What path difference is required to give:
(i) destructive interference?
(ii) constructive interference?

3. Why can’t you get a static interference pattern with two light bulbs while it is possible with two loudspeakers?

4. Light of wavelength 600 nm falls on a pair of double slits 0.5 mm apart.
Calculate:
(a) the fringe separation on a screen 1.0 m away from the double slits.
(b) the distance and direction  that the screen has to be moved to get the same fringe separation with light of wavelength 650 nm
5. A helicopter rises vertically above the sea 1 km from a radio transmitter. It is found that the radio reception varies in amplitude, maxima occurring every 10 m within the first 200 m above the sea. If the transmitter is 150 m above sea level explain this effect and calculate the wavelength of the transmitted radio signal.
6. A Young’s double slit experiment is carried out using green light. Describe and explain what will happen to the interference fringes produced if:
(a) red light is used
(b) blue light is used
(c) the two slits are moved closer together
(d) the two slits are moved further apart
(e) white light is used
(f) one of the slits is covered up
(g) a thin piece of transparent plastic is placed over one of the slits
(h) the slits are made narrower
7. Two speakers emitting a note of frequency 1 kHz are placed 2m apart on a table. Calculate the separation of the interference maxima along a line 10 m from the line joining the two speakers.

8. In a double slit experiment using monochromatic light the fringe width is measured 4m from the slits and found to be 4.5 mm. If the slit separation is 0.5 mm calculate the wavelength of the light used.

9. (a) Why is the diffraction of light in the visible area of the spectrum so difficult to observe?
(b) Does the fact that light shows interference prove that light is a wave, a transverse wave or both?

10. Why is it so much easier to show interference in the laboratory using a laser?

11. Draw a graph that shows the variation of intensity with position for the double slit experiment.

12. A laser beam of wavelength 620 nm is shone along a rod of glass so that part of the beam reflects from the near end and part from the far end. When the two beams combine they show interference due to the path difference formed by travelling along the rod and back. The rod is now heated gently, the end nearest the laser being fixed and the other end being allowed to expand. It is found that 15 fringes pass across the cross wires of an eyepiece used to view the pattern.
Calculate the increase in length of the glass rod.
(Ignore the effect of a phase change on reflection at one end for this question.)

13. Explain how interference might be useful in monitoring earth movements across a fault line.

14. Explain what difference, if any, you would observe if a double slit experiment using light were to be performed under water rather than in air.

15. A laboratory with a metal roof was found to be very noisy when it rained! How do you think interference would help solve this problem?

16. Describe how interference could be useful in testing the perfection of flat and curved glass surfaces.

17. A motorist drives along a motorway at a steady speed of 30 ms-1 between two cities listening to the car radio. As she travels along she notices that the radio signal varies in strength, 5s elapsing between successive maxima. Explain this effect and calculate the wavelength of the radio signal that she is tuned to.

18. In a double slits experiment using light of wavelength 580 nm fringes 0.75 mm wide are formed on a screen a distance of 3.5 m from the double slits.
Calculate:
(a) the slit separation
(b) the angular separation of the maxima in the pattern