How does the interference fringe width (distance between two maxima 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) & the screen?

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

• It was assumed that with the increase in diameter of the slit the fringe width will increase.
• It was also assumed that with the increase in refractive index of the medium the fringe width will decrease.

Justification

• Since the distance within which the slits were made was kept constant, with the increase in slit diameter the distance between the slits decreased, this further decreased the region of light waves superposing thus leading to greater area of illumination. Hence, the fringe width would increase.
• Since increase in refractive index would reduce the speed of light thus fringe width would decrease.

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.

• Black paper was used to make the slit.
• White paper was used to make the screen.
• String was used to mount the black paper on the burette stand.
• Different Medium: water, glass and glycerin

For variation of fringe width with respect to diameter of slit

• An opaque black paper was taken and two points were marked at a difference of 0.2 mm using a pen.
• Two holes were made with a needle of 0.05 mm.
• The black paper was placed and fixed on the experimental table using four strings that are tied at the four ends of the paper by making four holes at the ends. The other ends of the strings are tied to a burette stand.
• A red laser (λ=700nm) torch of 5mW power was taken and made fixed on the experimental table using a vertical clamp at a distance of 5 cm from the paper, such that it projects the light at the position of the holes or slits.
• At a distance of 1 meter from the paper, a white chart paper (optical screen) was set using four strings that are tied at the four ends of the paper by making four holes at the ends. The other ends of the strings are tied on the second burette stand.
• All the doors and windows of the room were closed and covered with black curtains; other lights of the room were turned off. This, ensured total darkness in the room.
• The laser was turned on.
• The pattern of light that was formed on the screen was observed.
• The distance between the central maxima and the first constructive interference was measured using a screw gauge and noted.
• The laser torch was turned off.
• At an interval of one minute, the laser torch was turned on and the distance between the central maxima and the first constructive interference was measured using the screw gauge and noted. This step was repeated three times.
• The paper with slits was then changed and the paper with the slits of diameter 0.05 mm was replaced by the paper with slit of diameter 0.06 mm.
• Steps 2 to 12 were repeated for 0.05mm to 0.09mm of diameter of the slit with a difference of 0.01mm and for each diameter three trials were taken.

For variation of fringe width with respect to refractive index

• An opaque black paper was taken and two points were marked at a difference of 0.2 mm using a pen.
• Two holes were made with a needle of 0.05 mm.
• The black paper was placed and fixed on the experimental table using four strings that are tied at the four ends of the paper by making four holes at the ends. The other ends of the strings are tied to a burette stand.
• A red laser (λ=700nm) torch of 5mW power was taken and made fixed on the experimental table using a vertical clamp at a distance of 5 cm from the paper, such that it projects the light at the position of the holes or slits.
• At a distance of 1 meter from the paper, a white chart paper (optical screen) was set using four strings that are tied at the four ends of the paper by making four holes at the ends. The other ends of the strings are tied on the second burette stand.
• All the doors and windows of the room were closed and covered with black curtains; other lights of the room were turned off. This ensured total darkness in the room.
• The laser was turned on.
• The pattern of light that was formed on the screen was observed.
• The distance between the central maxima and the first constructive interference was measured using a screw gauge and noted.
• The laser torch was turned off.
• At an interval of one minute, the laser torch was turned on and the distance between the central maxima and the first constructive interference was measured using the screw gauge and noted. This step was repeated three times.
• A glass slab was placed in between the laser torch and the white chart paper (screen) on the experimental table such that it covered the distance between the source and screen. Thus, the refractive index of the medium was changed.
• The distance between the central maxima and the first constructive interference was measured using screw gauge and noted and also the lateral shift between position of central maxima with and without medium (glass) was noted.
• Then the whole setup was inserted in a flat basin containing water and steps 2 to 12 were repeated.
• Then the whole setup was inserted in a flat basin containing glycerine and steps 2 to 12 were repeated.
• Thus, the same process was repeated for each material placed between the light source and the screen.