Since childhood, I have been intrigued by the colors of light I saw on the soap bubbles, the sky, and the window screen. Hence, I would always question “How and Why such patterns of light are created?” This led me to performing small experiments based on the topic of light as was taught in the Physics class. Physics is an integral part of life. All that we observe around us can be justified using physical experiments, laws and calculations. I believe that education takes place when there is a complete understanding of the topic along with the perfect amalgamation between theory and its application and the IB has always maintained a balance between the two. IB has groomed me to become an inquirer and this trait has motivated me to gather more information on the topics of physics. Last summer, I had joined a course in physics to know more about the interesting aspects of it. I was especially interested in the topic of wave optics which is an integral part of IB syllabus and asked “Can the colors of light observed in different situations be analyzed under this scope of wave optics?” One of the most interesting and important aspects of physics is optics. It deals with the interaction of light with objects around us. This led to further questioning myself -Can I experimentally obtain the natural phenomenon of light occurring around me?” This interest had driven me to perform a study on the double slit experiment. I learnt further from my in-depth study of Interference of light that it is an interesting domain as it invokes the wave-particle duality of matter and the theoretical field of quantum mechanics.
And when it comes to the point of contact between these physical domains, Young’s double slit experiment emerges as a prime example in the justification of a surprising optical phenomenon using the quantum theory and duality of matter. I thus decided to delve deeper into this field of study by going through several articles and deciding to come up with an original experiment myself that would aim to derive a relation between a few common aspects like refraction, interference. I thus finally stated my research question as:
My exploration is a deeper delve into other fundamental properties of wave optics such as interference, and refraction which I aim to make a part of this original experiment and thus deduce a correlation between these physical tendencies.
The process in which two or more light or electromagnetic waves of the same frequency combine to reinforce or cancel each other, the amplitude of the resulting wave being equal to the sum of the amplitudes of the combining waves. The effect is that of the addition of the amplitudes of the individual waves at each point affected by more than one wave. This results in constructive interference leading to formation of bright spots or destructive interference leading to formation of dark spots.
In this experiment light from a point source of a constant wavelength (laser light of red colour) is allowed to pass through two narrow slits in a dark room. This results in the formation of alternating dark and bright fringes of light (called interference pattern) on screen.
The figure is the schematic diagram of a Double slit experiment, where a monochromatic light acting as the primary source (marked in Red) is incident on the screen with two slits which acts as the two sources of light causing interference pattern. Light from these sources (two slits) behaves as a wave hence interferes constructively and destructively depending on the superposition of waves formed. On the optical screen these interfering patterns of light fall to give an illumination as shown in the front view. This consists of alternating bright and dark fringes which are equally spaced. This distance between the consecutive bright dark fringes are known as fringe width.
The central point midway between the two slits on the screen where waves coming from either of the slits constructively interfere and reinforce each other to form the brightest fringe in the pattern is called the central maxima. The other fringes on either side of the central maxima have the same intensity but are known as secondary maxima.
Fringe width is the distance between two consecutive bright spots (maxima, where constructive interference take place) or two consecutive dark spots (minima, where destructive interference take place).
Thus we can also say it is the linear distance between the central maxima and the next consecutive constructive interference
\(B=\frac{\lambda × D}{d}\)
where,
B is fringe width
λ is wavelength
D is distance between source and screen
d is the distance between two slits within which the diameters of slits are made.
The diameter of the slit is varied keeping the distance between the two extreme points of the two slits constant. Hence the distance between two slits “d” reduces.
The absolute refractive index of any given medium is defined as the ratio of the speed of light in vacuum to the speed of light in that medium. Refractive index of medium 1 with respect to medium 2 is the speed of light in medium 2 divided by speed of light in medium 1. It is similarly defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction at the interface of two transparent optical media.
In a black paper a fixed distance is marked within which two pinholes are made (S1 and S2) which act as the two slits. This is mounted with a laser of fixed wavelength acting as the primary source. As the light passes through the two slits interference patterns are observed on the white screen (optical screen) placed at a fixed distance D. The fringe width “B” is measured. The Refractive medium between the source and the screen is then varied to observe their effect on the fringe width in the interference pattern. The fringe width obtained is noted. The same thing is repeated thrice. Then the diameter of the slits was varied and the fringe width is measured for each diameter for three trials. This experiment is again repeated thrice and the data thus produced is noted.
In order to gain insight on the topic, a few previously conducted researches were consulted to identify the nature of experiments with polarizers. The paper titled, “The double slit experiment with polarizers” by M. Holden, D.G.C. McKeon, and T.N. Sherry inspired me a lot. The experiment thus performed helped realise the relationship between the polarizing angles and the refractive index of the medium. It also established that with an increase in the wavelength of the light incident, the fringe width would decrease. It helped me set up the experiment with both slits and variable refractive index. The plausibility of the experiment and the realizability of the aim was thus inferred.
Predictions
Justification
Refractive index of medium
Three different types of medium – glass, water and glycerin were chosen and the medium were one-by-one replaced and the resultant fringe widths were measured. These materials were used as medium since they were readily available at low cost and unlike plastic, do not cause much harm to the environment. Since the refractive index is a pure ratio hence has no unit.
Diameter of slit
Diameter of the double-slit was changed by using needles of different diameters, specifically 0.05mm., 0.06mm., 0.07mm., 0.08mm. and 0.09mm. For each diameter value, the experiment was performed thrice and the resultant data was obtained. These values were taken since both the slits had to fall inside the spot created by the laser pointer. As the pointer does not create a large spot, the slits could not have larger values for diameter. Also, for a greater diameter the particle nature of optics would be predominant hence fringes will not be observed. And it would not be feasible too, to make the slit of a diameter smaller than 0.05mm as it cannot be measured with the screw gauge at hand.
Fringe width
In this exploration, fringe width of the central maxima was taken as the dependent variable. It was measured by screw gauge and recorded thrice during every change in the independent variables. It was measured in millimeters (mm).
Distance between the two extreme points of the two slits
The diameter of the slit is varied keeping the distance between the two extreme points of the two slits at 0.2mm always constant. Hence the distance between two slits “d” reduces. This was the motive of our experiment.
Distance between the slit and screen
With an increase in the distance between the screen and slits, the fringe width would increase and hence, the observation of this exploration that the dependence of refractive index and the diameter of the slit would be disputed. To control that, the distance between the slits and the screen “D” has been kept constant at 1m ± 0.01m and measured using a ruler.
Wavelength of light used
As has been seen in the literature survey with an increase in the wavelength of the light incident, the fringe width would decrease and hence, the observation of this exploration that the dependence of refractive index, and the diameter of the slit would be disputed. To control this wavelength of light, a laser torch of the same colour (λ=700nm) was used in all the trials.
For variation of fringe width with respect to diameter of slit
For variation of fringe width with respect to refractive index
Safety Precautions
Ethical Considerations
Environmental Considerations
Formula used
Mean = \(\frac{Σ(trial \,values)}{number \,of \,trials}\)
Standard deviation (SD) =√ \(\frac{Σ(trial \,values-mean\, value)^2}{number \,of \,trials}\)
Key: R.I = Refractive Index
Sample calculation
For water,
Average fringe width of the medium = \(\frac{3.02+3.23+3.41+3.63=3.83}{5}\)= 3.42 ± 0.01 mm
Error propagation
For Row - 1 of Table - 4
Percentage error in mean fringe width for water = \(\frac{absolute\,uncertainty}{value\, of\,mean\,fringe\,width}\)× 100
=\(\frac{±0.01}{3.02}\)× 100 = ± 0.33
Percentage error in mean fringe width for glass = \(\frac{absolute\,uncertainty}{value\, of\,mean\,fringe\,width}\)× 100
=\(\frac{±0.01}{3.04}\)× 100 = ± 0.32
Percentage error in mean fringe width for glycerin = \(\frac{absolute\,uncertainty}{value\, of\,mean\,fringe\,width}\)× 100
=\(\frac{±0.01}{3.05}\)× 100 = ± 0.32
Percentage error in diameter = \(\frac{absolute\,uncertainty}{value\, of\,mean\,fringe\,width}\)× 100
=\(\frac{±0.01}{0.05}\)× 100 = ± 20.00
The equation of trendline of fringe length with respect to diameter of slit for water is:
y = 20.2x + 2.01 ... ... ... (equation 1)
The equation of trendline of fringe length with respect to diameter of slit for glass is:
y = 14.5x + 2.315 ... ... ... (equation 2)
The equation of trendline of fringe length with respect to diameter of slit for glycerin is:
y = 10.3x + 2.525 ... ... ... (equation 3)
y = - 0.8797x + 4.5947 ... ... ... (equation 3).
Scientific justification:
From the first graph we see the fringe width increases with increase in diameter of slit which is justifying the dependency on separation between slits. This is because as the diameter increase in two slits within the given constant length 0.20 mm it leads to decrease in the distance of separation between the slits (d). As more and more waves diffract through the increasing aperture, the fringe width increases too.
Thus, we can infer
Hence,
Fringe width ∝ \(\frac{1}{Distance\, between \,the \,sites}\)
From the second graph, it is observed that the fringe width decrease with increase in refractive index, which might be due to the fact that light waves travel slower in media of increasing refractive indices as the resistance to flow of waves increases with increase in optical density, thus decreasing the velocity of light waves. Thus, the wavelength decreases too. and conversely the fringe width increases. Thus
\(\lambda=\frac{\lambda}{\mu}\)
Fringe width ∝ λ
Fringe width ∝ \(\frac{\lambda}{\mu}\)
Fringe width ∝ \(\frac{1}{\mu}\)
where,
ƛ is changed wavelength
ƛ is wavelength
μ is refractive index
How does the interference fringe width (distance between two maximas i.e. two bright spots) depend on the diameter of the slits (behaving as source), refractive index of medium present between the source of the light (double slit) and the screen?
y = 20.2x + 2.01
The equation of trendline of fringe length with respect to diameter of slit for glass is:
y = 14.5x + 2.315
The equation of trendline of fringe length with respect to diameter of slit for glycerin is:
y = 10.3x + 2.525 ... ... ... (equation 3)
It is thus observed that there is a straight-line graph obtained for all the mediums (of different refractive index) each having an intercept value almost of the same order.
It is also observed that the slope of the graph decreases from 20.2 to 10.3 as the refractive index increases from 1.33 to 1.50 which justifies the equation:
\(B = \frac{\lambda× D}{d}\) and the relation Fringe width ∝ \(\frac{1}{\mu}\)
There are nearly no outliers thus the graph shows a perfect positive correlation. This can be justified by the high value of regression coefficient (= 0.999). The fringe width is seen to be increasing with increase in diameter.
The equation of trendline of fringe length with respect to refractive index is obtained as:
y = - 0.8797x + 4.5947
The negative slope indicates fringe width is inversely related to refractive, justifying the equation:
Fringe width ∝ \(\frac{1}{\mu}\)
The graph shows a negative correlation. This can be justified by the high value of regression coefficient (= 0.95). The fringe width is seen to decrease with increase in refractive index.
Thus, we finally conclude that the interference fringe width (distance between two maxima i.e. two bright spots) depend directly on the diameter of the slits (behaving as source) and inversely on refractive index of medium present between the source of the light (double slit) and the screen, keeping the length within which, the two slits have to be made constant, distance between the source and screen, and wavelength of source of light also constant.
Systematic error
It increases the fringe width during measurement since the precision is 0.01mm only. It can be corrected by using a travelling microscope to measure the fringe width.
Because of this, the light may shift from the exact position of the slits. It can be corrected by using a properly aligned and efficient laser pointer, mounted in a sturdier tripod.
Methodological error
This experiment could again be conducted focusing more on the variation in fringe width due to a variation in the angles between the polarizers. Since a slight relation could be ascertained, a deeper and more extensive study would provide better justification for changes in fringe width observed due to change in not just mutually horizontal angles but even mutually vertical angles. The research question could thus be framed as: How does the fringe width between central maxima and consecutive secondary maxima vary with the change in position of polarizers kept mutually horizontal and vertical by turning the two by different angles during a double slit experiment? To perform the exploration, firstly, a black paper could be taken and two pinholes could be made, before mounting it before another black screen and a laser is to be fixed so as to let the light pass through them and four objects (polarizers) to be kept between the source and the screen to observe their effect on the fringe width in the interference pattern thus generated. The polarizers could then be mutually rotated vertically and horizontally and the change in position of pattern and fringe width could be noted.
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