Terms to take note:
Central maximum : central bright fringe, widest and brightest among the bright fringes (maxima)
m^{th} intensity minimum : For singleslit. Ranges from ±1, ±2, ±3, …, ±n. Positive when above or right of the center of pattern, negative when below or left of the center of pattern.
m^{th} intensity minimum : For doubleslit. Ranges from ±1, ±2, ±3, …, ±n. Positive when above or right of the center of pattern, negative when below or left of the center of pattern.
diffraction envelope : the outline of the singleslit diﬀraction pattern
We are all familiar that light has a dual nature; it can behave as a particle or a wave. Diffraction occurs when a wave encounters an obstacle or a slit that is comparable in size to its wavelength, whereas Interference is the phenomenon where waves meet each other and combine constructively or destructively to form composite waves. The main difference between the two is that diffraction involves a wave and some obstacle which deflects the wave or bends it and interference involves a wave which combine with other waves.^{[1] }
However, fundamentally, these two phenomena are the same, as they both arise from wave interference that follows the principle of superposition which states that when waves encounter each other, they can either add up (constructive interference) or cancel each other out (destructive interference), depending on the properties of each wave.^{[2]}
The objective of this experiment is to quantitatively relate the singleslit and doubleslit diffraction pattern obtained to the slit width. Also, to differentiate the patterns produced by singleslit and doubleslit diffraction and determine the quantitative relationship between a doubleslit diffraction pattern and the corresponding slit separation.
The experiment started by assembling the optical materials like the one in Figure 3. Slit and pattern were of the same level vertically .The first part of the experiment was the singleslit diffraction. Here, 0.004 mm, 0.002 mm, and 0.008 mm width single slit were taken into account. Boundaries of dark fringes on white sheet were marked and important data were recorded and calculated in Table W1 and W2. The second part was the doubleslit interference I: calculating the slit width. Here, the double slit with 0.04mm slit width and 0.25mm slit separation were selected. Boundaries of dark fringes in the diffraction envelope were marked on the white sheet. Important data were recorded and calculated in Table W3. The last part pf the experiment was doubleslit interference II: changing the slit width and slit separation. Here, we considered 4 doubleslits combination which can be found in Table W4. The number of interference fringes located inside the central maximum were counted and the width of the central maximum were recorded. Important data were also calculated in Table W4.
Table W1. Wavelength of the laser diode
a = 0.02 mm, m = 1 
a = 0.04 mm, m = 1 

Distance between side orders, Δy_{1} 
143 mm 
61.6 mm 
Distance from center to side, y_{1} 
71.5 mm 
30.8 mm 
Calculated wavelength  7.7089 x 10^{4}mm 
6.6415 x 10^{4}mm 
Percent difference 
18.60% 
2.18% 
Average wavelength (λ) 
7.1752 x 10^{4}mm 

Slittoscreen distance (L) 
1855 mm 
In Table 1, the wavelength was calculated using the equation:
y_{m,diff }= mλLa^{1 (1)}
Rearranging Equation 1,
λ = a y_{m,diff }m^{1}L^{1 (2)}
where λ corresponds to the wavelength, a is the singleslit width, y_{m,diff }is the distance from center to side, m is the intensity minimum, in this case, ±1, L is the distance from slit to screen. Distance between side orders , Δy_{1}, was measured between the first order (m = ±1) minima. The measurement started at the midpoint of the dark fringes. Dividing it by two, you’ll get the distance from center to side, y_{m,diff.}
Theoretical wavelength is 650 nm or 6.5 x 10^{4}mm. It can be observed that in the second column (a = 0.002 mm, m =1), the percent difference is relatively high but in the third column (a = 0.004 mm, m =1), percent difference is relatively low. Percent difference for the average wavelength is 10.5 %. Possible source of error may come from slightly different vertical level of slit and pattern in which the small angle of inclination gave rise to a slightly different lengths of fringes.
Increasing the wavelength of the laser would increase the width of the fringes as suggested by Equation 2. Also, placing the screen farther from the slit would have a larger value of L in which case would also give rise to an increase in width of the fringes.
Table W2. Data and results for the 0.04 mm single slit
m = 1  m = 2  
Distance between side orders,  61.6 mm  130 
Distance from center to side  30.8 mm  65 
Calculated wavelength 
6.6415 x 10^{4 mm} 
7.0081 x 10^{4mm} 
Percent difference  2.18%  7.82% 
The procedure and equations used in Table W1 were the same in Table W2 only that the secondorder minima (m = ±2 ) was taken into account. The percent differences in Table W2 are relatively low making the data acceptable.
Figure W1. Sketches of diffraction pattern for various slit widths and fixed slittoscreen distance
In Figure W1, you can see the obtained measurements of the diffraction patterns perfectly labeled. The widest is the central maximum, it is the brightest fringe. As you move away from the central maximum, the brightness and the width decreases. In between the bright fringes are the dark fringes in which destructive interference occurred. To understand more, take a look at Figure 4 below. You can also observe that the firstorder minima have the same values for both the left and the right side, the same goes with secondorder minima. Also, in Figure W1, as the slit width is decreased, diffraction envelope became smaller.
In Figure 4, the highest crest gives rise to the brightest fringe which is the central maximum. The crests in Figure 4 are the bright fringes while the troughs are the dark fringes. You can see that the crest’s height goes shorter and shorter as you move away from the center, this corresponds to the decreasing brightness of the fringe as you move away from the center.
Table W3. Data and results for the a = 0.04 mm, d = 0.25 mm double slit
m = 1  m = 2  
Distance between side orders,  70 mm  136 mm 
Distance from center to side  35 mm  68 mm 
Calculated slit width  0.03803 mm  0.03914 mm 
Percent difference  4.925%  2.132% 
Slittoscreen distance (L)  1855 mm 
In Table W3, slit width was calculated using the equation:
y_{m,diff }= mλLd^{1 (3)}
Rearranging Equation 3,
d = mλL y_{m,diff}^{1 (4)}
Equation 3 is similar in form with Equation 1 with the slit width, a, replaced by the slit separation, d. However, Equation 1 gives the position of intensity minima in a singleslit setup while Equation 3 gives the position of intensity maxima in a doubleslit setup.
Taking the average wavelength obtained in Table W1, the percent differences are relatively low. Thus, the values obtained are valid.
In this part of the experiment – doubleslit interference I, diffraction envelope was observed. Inside the diffraction envelope are equally spaced dark and bright fringes but of different brightness.
In doubleslit interference, the width of the interference fringes are controlled by the slit separation, d. On the other hand, the diﬀraction envelope is controlled by the slit separation, a.
Similar to the one stated in Table W1, nncreasing the wavelength of the laser would increase the width of the fringes as suggested by Equation 4. Also, placing the screen farther from the slit would have a larger value of L in which case would also give rise to an increase in width of the fringes.
Table W4. Data and results for doubleslit interference II
a = 0.04 mm
d = 0.25 mm 
a = 0.04 mm
d = 0.50 mm 
a = 0.08 mm
d = 0.25 mm 
a = 0.08 mm
d = 0.50 mm 

Number of fringes  13  25  5  11 
Width of central maximum  61.5  61.5  28.2  28.2 
Fringe width  4.73  2.46  5.64  2.56 
In Table W4, it can be seen that the larger the slit separation d in the same slit width, a, the greater the number of fringes and the width of central maximum remained unchanged. Theoretically, the diffraction envelope is independent of the slit separation. However, the interference fringes are dependent of the slit separation. The larger the slit separation, the greater the number of the interference fridges, the smaller the fringe width. And our observation agreed with this.
Figure W2. Sketches of interference pattern for various slit widths and slit separation
In Figure W2, you can see the obtained measurements of the diffraction patterns in a diffraction envelope perfectly labeled. The small fringes are assumed to be of equal widths. The intensity of light in these fringes varies. The end ones are the dullest while the center is the brightness. To see how this works, take a look at the Figure 5 below.
Figure 5 shows how the dashed line or the interference envelope groups the fringes. This is similar to the singleslit pattern (left). You can see that inside the envelope are smaller singleslit patterns, this is the reason why the brightness of the fringes varies (right).
If light were to behave as a particle for the single slit and double slit, the pattern would look like the one in Figure 6, not that far when light behaves a a wave. The concentrated regions give rise to your constructive interference or the bright fringes while the barren or not concentrated regions are your destructive interference or the dark fringes. The central maximum have the most concentrated region which is the middle part horizontally from Figure 6.
REFERENCES:[1] Nikos M. (http://physics.stackexchange.com/users/44176/nikosm), What is the difference between diffraction and interference of light?, URL (version: 20140929): http://physics.stackexchange.com/q/137863
[2] Subodh Ghulaxe (http://physics.stackexchange.com/users/22316/subodhghulaxe), What is the difference between diffraction and interference of light?, URL (version: 20140929): http://physics.stackexchange.com/q/137865
[3] Tipler, P., Physics for Scientists and Engineers, 4th ed., W.H. Freeman & Co., USA (1999)
[4] http://www.perceptions.couk.com/uef/imgs/2slit3.gif
SAMPLE CALCULATIONS:
For Table W1:
λ = a y_{m,diff }m^{1}L^{1} = (0.02 mm)(71.5 mm)/(1)(1855mm) = 7.70819 x 10^{4 }mm = 771 nm
For Table W3:
d = mλL y_{m,diff}^{1 }= (2)(7.1752 x 10^{4}mm)(1855mm)/(68mm) = 0.03914 mm
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