Interference

“What happens to the waves after the interference?”

The duality of the nature of light, a particle and a wave, makes it interesting.. and complicated.  Light, being a wave,exhibits interference, the adding up (constructive) or cancelling out (destructive) of waves as they superpose each other, depending on the properties of the waves.

Image Source: http://www2.mcdaniel.edu/Biology/PGclass/hearing%20noise/infrnctx.html

Constructive interference happens when two waves encounter in phase, that is, they have the same frequency and they travel along the same direction, resulting to a bigger wave with a larger amplitude. On the other hand, destructive interference happens when two waves that come together are out of phase, that is, they travel along the opposite direction, cancelling each other out.

When light waves pass through a slit or an object, the waves bend and spread out past the openings creating patterns of dark bands (destructive interference) and bright bands (constructive interference). This phenomenon is called diffraction.

The experiment aims to

  • investigate the patterns made by single-slit diffraction and double-slit diffraction
  • quantitatively relate the single-slit and double-slit diffraction pattern to the slit width
  • determine the relationship of the double-slit diffraction pattern and the slit separation

Caution!

  1.  Do not look directly into the laser beam.
  2. Do not touch the slits with your fingers or any other instrument including pencils and pens.
  3. Do not hit other people with the laser beam.

For the experiment setup, the laser is placed at one end of the optical bench. About 3 cm in front the laser is the single slit disk and attached on the wall is a white sheet of paper as the slit screen that the laser beam should hit. The laser diode should be adjusted using the knobs at the back in such a way that the beam is centered on the slit. The distance between the slit and the screen was measured and recorded in the table as L. Mark the locations of the intensity minima and the dark fringes boundaries for every part.

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And, lights off!

Single Slit Diffraction

The first part of the experiment is the single slit diffraction. When light waves pass a single slit of width a, the waves form a diffraction pattern of dark and bright fringes, which is symmetric about the center, visible at a distance L from the screen. The central maximum, set at y = o, is the center of the brightest fringe. As you move away the central maximum, the brightness  decreases. The fringes at the central maximum are of equal width at small values of ϴ. The slit width a can be calculated using

                                                           a = mλL/y(m, diff)                                                                      (1)

where m is the intensity minimum, λ is the wavelength, slit-to screen distance, and y is the distance from center to side.

table 1

Table 1 shows the measured distances between the side orders and the distance from the center to side at slit width set at 0.02 mm and 0.04 mm, first order minimum. The wavelength was calculated using (1). It can be seen that the smaller slit width gained a larger wavelength with a value of 818.7 nm and 675.4 nm, which yielded 25.95% and 3.91% difference with respect to the theoretical wavelength 650 nm. The large deviation of the 0.02 mm slit width may have been caused by the constraints in manufacturing of the slit, the marking of the boundaries of the fringes since lights are off, and the measurement of the distances.

Figure 1. (left) 0.02 mm slit width, (right) 0.04 mm

From table 1 and figure 1, it can be implied that as the slit gets wider, the wavelength tends to be shorter. As the slit width gets narrower, the first order intensity minima tends to be less visible.

table 2

For table 2, the slit width was set at 0.02 mm and 0.04 mm but this time, both the first order and second order intensity minima were considered. The distance from center to side was obtained by dividing the measured distance between side orders into two. The wavelengths were calculated using (1) and compared to the theoretical wavelength 650 nm.

It could be seen here that still, the 0.02 mm slit width, both first order and second order minima, obtained longer wavelengths than those of 0.04 mm slid widths, although it deviated larger possibly caused by the marking of the boundaries and measurement of the distances.

Double-slit interference I: Calculating the slid width

The second part of the experiment used a double-slit disk instead of a single-slit disk. This part of the experiment aimed to investigate the double-slit width pattern and to relate quantitatively the double-slit diffraction pattern and the slit width.

When light waves pass through a double slit, the light diffracts and the interferes resulting to a double-slit interference and single-slit diffraction. The outline of the single-slit diffraction pattern, called the diffraction envelope, is still visible with equally spaced dark and bright fringes but with unequal brightness. At a small slit separation d, there will form alternating series of dark fringes and bright fringes.

Figure 2. (left) single-slit pattern, (right) double-slit pattern

As shown in figure 2, the bright fringes in the double-slit pattern has equal brightness unlike the single-slit pattern.

For the double-slit, the position of the intensity maxima is given by

                                                             y (m, int) = mλL/d                                                             (2)

This may look similar to (1) with the slit width a replaced by the slit separation d but (1) calculates the intensity minimum if arranged, and (2) gives the intensity maximum.

table 3

Table 3 shows the calculated distance from center to side, which is half of the measured distance between side orders for the slid width of theoretical value 0.04 mm and a slit separation of 0.25 mm double slit. The calculated slit widths 0.035 mm for the first order minimum and 0.0326 for the second order minimum deviated 12.50% and 18.60% with respect to 0.04 mm, which is the theoretical value.

Unfortunately, I can’t upload the video of the slit pattern when the slit separation was varied from 0.125 mm to 0.75 mm. I can be seen from there that as the slit separation is increased, the fringes increased in number and got smaller.

Double-slit interference II: Changing the slit width and the slit separation

The last part of the experiment still involved double-slit interference but the slit width and the slit separation are varied. In the double-slit interference, the width of the interference fringes are dependent on the slit separation d while the diffraction envelope is dependent on the slit separation a.

table 4

Table 4 is the tabulation of the counted number of fringes, measured width of central maximum, and the fringe width calculated by dividing the width of the central maximum by the number of fringes since the interference fringes are equally spaced. It could be implied from here that both at a narrower slit width, 0.04 mm, and wider slit width, 0.08 mm, there are more number of fringes at the narrower separation of slit than at the wider slit separation.

To conclude for this part:

  • Increasing the wavelength of the laser for the double-slit interference and the single slit diffraction, which is proportional to the slit width, the lower the number of fringes and the higher the fringe width
  • Placing the screen farther from the slit for the double-slit setup, which means increasing L, the number of fringes will decrease and get bigger.

 

Thing with interference, after the encounter, the waves will just move on as if nothing happened.

 

References:

[1] Tipler, P., Physics for Scientists and Engineers, 4th ed., W.H. Freeman & Co., USA (1999)

[2] Instruction Manual and Experiment Guide for the PASCO scientific Model OS-8523

[3] Young, Hugh, and Roger Freedman. University Physics with Modern Physics 13th edition. Pearson Education Inc, 2004.

 

 

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