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Engineering Physics Lab Experiments

To determine the wavelength of given laser source by plotting diffraction minima’s



Aim

To determine the wavelength of given laser source by plotting diffraction minima’s.

Apparatus Required:

Track and screen from the Basic Optics System, Laser source, Single Slit Disk, Screen white paper, Graduated Scale.

Description:

Since the work of Thomas Young, about 1800, light has been thought of as a wave. One can, therefore, speak of the amplitude and phase of a light wave at any point in space. As like any other wave, two or more light waves may interfere at any point to give either an increase or decrease in wave amplitude at that point. When a light wave encounters an obstacle, the light interacts with the material of the obstacle. As a result, the amplitude and phase of the wave is partly changed. The modified part of the wave may then interfere with the rest of the wave, producing a pattern of light and dark. These effects are not usually noticeable because we deal with obstacles large compared to a wavelength, and we do not closely examine the shadows cast by such objects. In that case, a ray picture is quite adequate. If we use a very small obstacle, or look carefully at the shadow, we will see the effects of interference between various parts of the wave. In the laboratory, it is possible to make a small slit. When the obstacle is illuminated by a small light source a screen placed near the slit will show the expected shadow pattern of a bright line on a dark background. As the screen is moved away from the slit, the pattern becomes more complicated, due to the interference of the parts of the wave that interact with the slit edges. At very large distances, one sees an array of bright lines, spaced at regular intervals. Laser light is much more coherent than light from conventional sources. So that one may observe interference effects even when the path difference between the interfering rays is much greater than 109 wavelengths. Figure -1 is schematic of the apparatus used to observe this effect.

Observing diffraction

Fig. 1. Arrangement for observing diffraction with slit and point source An exact calculation of the diffraction pattern for the situation we have been considering more generally the angle to the maxima (bright fringes) in the interference pattern is given by

d sin θ = mλ (m = 0,1,2,3,. )

λ= a

sin θ/m

Where d is the slit separation, λ is the wavelength of the light, and m is the order 0 for the central maximum, 1 for the first side maximum, 2 for the second side maximum,. counting from the center out?. Since the angles are usually small, it can be assumed that

sin θ≈tan θ

Single slit diffraction of laser beam

Set Up:

Optics bench se up for single slit diffraction

Procedure:

  1. Set up the laser at one end of the optical bench and place the single slit disk in its holder (about 3 cm) in front of the laser. Orient the optical bench so the laser points toward the wall (see figure-3).
  2. Set up the white screen at the other end of the bench. Cover the screen with a sheet of white paper.
  3. Select the appropriate slit width (about 0.04mm) by rotating the slit disk until the slit is centered in the slit holder.
  4. Adjust the position of the laser beam from left-to-right and up-and-down until the beam is centered on the slit.
  5. To get perfect diffraction pattern adjust the length between source and slit and to see the pattern clearly this should be performed in the dark room.
  6. Determine the distance from the slit to the screen (D). Note that the slit is not aligned with the center of the holder.
  7. With the room lights off, mark of the positions of minima in the diffraction pattern on the screen(graph sheet). Label the order of the minima m = 1,2, etc. and also central maxima.
  8. Sketch the diffraction pattern in the lab notebook.
  9. Remove the single slit carefully and find its width of the slit using travelling microscope without disturbing the slit width. Let it be ‘a’ cm.
  10. Remove the graph paper, using this measure the distances between the first minima’s and note the half of this values. Let it be ‘r1’ from first minima where m=1.
  11. Again measure the distance between the second minima‘s let it be ‘r2’ from second minima m=2
  12. Repeat the procedure for different minima’s.
Fringe pattern of single slit

Observations:

Least count =1 ????????????/???????? ???????????? ???????? ???????????????????????????? ????????????????????

To find the slit width of the first slit.

S. No M.S.R. V.C. MSR+(LC) VC
1
2
3

S1 =---------------------cm

To find the slit width of the second slit.

S. No M.S.R. V.C. MSR+(LC) VC
1
2
3

To determine the wavelength of laser source

Slit width ‘a’ cm Order of diffraction (m) ‘r’ cm sin ???? ????= √????2 + ????2 ???? sin ???? ???? = ????
S1
S2

Precautions:

  1. Under any circumstance do not look directly into the laser beam.
  2. Do not shine the laser toward anyone.
  3. Adjustment of slit, laser must be made properly so that fringes are bright and distinct.
  4. Since the linear shift d is proportional to D, it should be fairly large (around 1 meter)
  5. Make sure that a strong monochromatic source of light is used.

Result:

The wavelength of given laser light is--------------------

Reference Books:

  1. ”The Feynman Lectures In Physics”,R.P.Feynman,R.B. Leighton and M.Sands,Addison Wesley ,1963
  2. Experiments In Modern Physics”,A.C.Melisson,Academic Press,N.Y. 1966
  3. ”Optics”, A.Ghatak, Tata McGraw Hill, New delhi,1992