To what extent does increasing the density of saline solutions, ranging from 0g/mL to 35g/mL in 5g/mL increments, impact its refractive index when measured with yellow light at an angle of incidence of 45 degrees using a hollow prism?

My research is centred around the relationship between the density of saline solution and its refractive index (RI). Growing up, swimming was a sport I regularly engaged myself in. It was always exciting to swim on a hot day, and even more exciting when we could free swim after training. A common game we would play during free swimming was finding toys or coins that had been thrown into the pool. During many sessions, I realized that the coins often looked closer or further away than they seemed, tricking us when we tried to dive for them. It was fascinating how the water made toys and coins look as though they shifted positions within the pool, with the coins looking closer when they were farther away and vice versa. This is where I began to notice how water as a medium undergoes scientific phenomena like refraction. When we experimented in class with glass prisms to observe the factors that affected reflection and refraction, I understood that it was the same effect that happened to the coins and toys at the bottom of the pool. I noticed that the magnitude of the refraction of tap water, which is what we were using in class, was less than the refraction in the pool. This made me wonder how the density of mediums influences the refractive index. The pool can be considered to be slightly denser than the distilled water because of the added chlorine. To explore this relationship, I chose to investigate how different densities of saline solution impact the refractive index. I chose saline solutions because it would be easy to control the density of the solution by simply increasing more salt in the water so that I could see the effect of density on the refractive index. The mass of salt will determine the density, which in turn will show how much the saline solutions will refract.

While researching I found two ways to conduct my experiment. The first experiment included using a plane mirror and needle, where you use a convex lens and find its focal length, placing a plane mirror on a horizontal stand, and then placing the lens on the mirror. Next, you screw an optical needle in the stamp, holding it horizontally above the lens. The essence of this method is bringing the tip of the needle to the principal vertical axis of the lens so it seems like it's touching the tip of its image. Lastly, it involves moving the needle vertically, removing the parallax between the needle and its image and lastly measuring the distance between the tip and upper surface of lens (Byjus, 2022). I did not choose this method, rather I used the method of shining light through a hollow prism filled with liquid (which will be my saline solution) instead, because I believed the first one would cause a lot of random error, impacting the precision of my experiment.

→ Light, more specifically visible light, is a form of electromagnetic radiation composed of particles known as photons that can't be detected by the human eye (Oxford Instruments, 2023), which carry energy and travel with a constant speed (c) of \(3 \times 10^8 \mathrm{m}/\mathrm{s}^{-1}\) in a vacuum. As light interacts with the environment and matter around it, the photons alter, dispersing, bending, reflecting, and refracting.

→ A refractive index (further abbreviated as RI) is the ratio of velocity of light in a vacuum to its velocity in a specific medium (StudySmarterUK, n.d.). The refractive index (symbol: n) determines the speed of light in a medium apart from a vacuum. Travelling through other media aside from a vacuum changes its speed depending on the number of particles the photons have to interact with. It is a unitless quantity expressed through real numbers and is influenced by factors such as temperature, pressure, and wavelength. It is commonly measured using devices like refractometers or spectrometers, which quantify the bending of light as it passes through a material. This quantity is used in many fields, specifically submarine optics and aquatic studies. For example, submarines use periscopes and other instruments to see above the water's surface while submerged. Similarly, researchers studying aquatic environments and oceanography use the refractive index of water to correct for distortions in underwater photography and remote sensing data. This improves accuracy, which in turn helps in understanding and researching the ocean.

The refractive index can be calculated through \(\mathbf{n}=\frac{c}{v}\), where
\(\mathbf{n}=\) refractive index of the medium
\(\mathbf{c}=\) speed of light in a vacuum \((3.00 \times 10^8) \mathrm{m}/\mathrm{s}^{-1}\)
\(\mathbf{v}=\) speed of light of that medium \((\mathrm{m}/\mathrm{s})\)

Or snells law, denoted as

\[\begin{gathered} n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \\ \text{where} \\ n_1 - \text{refractive index of the first medium} \\ \sin(\theta_1) - \text{angle of incidence} \\ n_2 - \text{refractive index of the second medium} \\ \sin(\theta_2) - \text{angle of refraction} \end{gathered}\]

But from a research done from Hit Kumar, an alternative formula to calculate RI is shown below which I will be using in this experiment

\[\text{Refractive Index} = \frac{\sin(\frac{A+D}{2})}{\sin(\frac{A}{2})} \text{ (Equation 1)}\]

where
A is Angle of Prism (\(60^\circ\))
D is Angle of Deviation
(Hit Kumar, n.d)

→ Density, put simply, is the number of particles per volume. Density is measured in units such as kilograms per cubic meter \((\mathrm{kg}/\mathrm{m}^3)\) or grams per cubic centimetre \((\mathrm{g}/\mathrm{cm}^3)\). Density affects the buoyancy of objects in fluids, determines the behaviour of materials under different conditions, and allows us to understand the composition of substances. It can be influenced by factors such as temperature, pressure, and composition. Methods for measuring density include using instruments such as graduated cylinders or displacement methods. To calculate density, we can use

\[\rho = \mathbf{m}/\mathbf{v}\]

Where \(\rho\) is density in \(\mathrm{g}/\mathrm{cm}^3\)
\(m\) is mass in \(g\)
\(v\) is volume in \(\mathrm{cm}^3\)

→ The link between density and refractive index can be expressed through the Gladstone-Dale equation. The Gladstone-Dale law, also known as specific refraction, provides a relationship between the refractive index and the density of a medium (Barthelmy, n.d.). The Gladstone-Dale equation, first originated from experiments conducted by Henry Enfield Roscoe, John William Strutt, and Thomas Graham, is applied in fields like optics, chemistry, physics, and engineering, as the measures of density and refractive index also manifest in these fields as aforementioned (Christopher T. Wanstall, Ajay K. Agrawa, & Joshua A. Bittle, 2020, p. xx).

→ The Gladstone-Dale law is given by:

\[\frac{n-1}{\rho}=k \text{ (Equation 2)}\]

where
\(\mathbf{n}\) is the refractive index
\(\rho\) is density
\(\mathbf{k}\) is a constant depending on the material

Rearranging this formula for \(n\), we get \(n=k\rho+1\) (Equation 3)
This equation gives us a straight linear line, which can then be used to formulate a predicted theoretical graph (fig 1). This will tell us that as the refractive index increases, density will also increase. It reveals that they are directly proportional factors.

To what extent does increasing the density of saline solutions, ranging from \(0 \mathrm{g}/\mathrm{mL}\) to \(35 \mathrm{g}/\mathrm{mL}\) in \(5 \mathrm{g}/\mathrm{mL}\) increments, impact its refractive index when measured with yellow light at an angle of incidence of 45 degrees using a hollow prism?

If the density increases, then the refractive index will increase. This is because if density increases, then the number of particles per unit volume increases. This is the result of more salt being added to the saline solution, as more salt particles obstruct the photons of light as they pass through the solution, thus resulting in the beam bending closer to the normal and ultimately increasing the refractive index. This is assuming that the angle of incidence stays constant, a factor that impact the refractive index as described by the Gladstone - Dale equation. When a wave of light passes through a certain medium, the density of that medium dictates how it moves next; in mediums which have higher density like glass, we see that the refractive index is higher, and when it is lower like through air, it has a lower refractive index. This observation tells us that the refractive index is directly proportional to the density and that the arrangement and number of particles within the medium impact the refractive index. I predict that there will be a deviation in the linear graph on the y-intercept; the line will begin from 1.33 because the refractive index of plain water is 1.33. The gradient of this graph will give us the Gladstone Dale constant for the saline solution which we can use to prove whether the relationship is truly linear.

Be sure the ray of light is not shined in someone's eyes. A bright light like that can damage eyesight (Gerstein Eye Institute, 2021). To avoid this, do not play around with the ray box and keep it on the table.

Make sure all electrical devices are away from water. If it spills, it may wet the wires, causing an electrical shock (Kubitz, 2022). Keep tissues on standby to ensure that spilt water can be cleaned up.

Be sure not to mishandle the ruler. If poked or slapped with it, it may cause pain.

In order to reduce the wastage of materials, more specifically save on wasting water and salt, the saline solutions can be collected. This can be used in other experiments such as seeing the impact of concentration of a solution on RI etc. Apart from this, there are no other ethical or environmental considerations.

[1] Teat dropper
[1] Ray Box (570nm wavelength)
[1] Beaker (\(\pm 5 \mathrm{ml}\))
[1] Pen/Pencil to record data
[1] Paper to record data
[1] Spoon to stir the solution
[1] Density bottle
[1] Foam board
[1] Ruler
[1] Protractor (\(\pm 5^\circ\))
[1] Weighing balance (\(\pm 0.01\))
1.75 litres of distilled water (\(\pm 5 \mathrm{ml}\))
\(35 \mathrm{g}\) of salt (\(\pm 0.01\))
Tissues

1. Clean and dry the density bottle thoroughly.
2. Weigh the empty and dry density bottle (\(m_1\)).
3. Fill the density bottle with plain water, ensuring it is filled without any air bubbles. Weigh the filled density bottle (\(m_2\))
4. Remove the plain water and was and dry it thoroughly. Add your solution.

5. Find mass of solution (\(m_3\))
6. Find mass of plain water, calculate \(m_2-m_1\)
7. Find the volume of the bottle by using the formula \(\frac{m_{\text{plain water}}}{\text{density of water}}\)
8. To find the mass of saline solution, do \(m_3-m_1\)
9. Density is Mass over volume, therefore do \(\frac{m_3-m_1}{\text{volume of bottle}}\)
(Science Sir, 2022)

10. Pin plain white paper on the foam board with the help of the pins.
11. Trace the prism and mark the outline as ABC.
12. On the side AB, draw a normal.
13. Draw the angle of incidence at 45° following the normal
14. Put the prism filled with saline solution, on the marked outline ABC. Ensure no air remains inside. Use a teat dropper to carefully fill the prism.
15. Set your ray box and shine it from the 45° angle drawn.
16. Mark the emergent ray on the other side of the prism with a ruler
17. Repeat steps 1-7 with the next increment.
(Hit Kumar, n.d., p. xx)

18. Use the formula to calculate the refractive index of the saline solutions.

\[\text{Refractive Index} = \frac{\sin(\frac{A+D}{2})}{\sin(\frac{A}{2})}\]

where
A is Angle of Prism (\(60^\circ\))
D is Angle of Deviation
(Hit Kumar, n.d., p. xx)

19. Calculate and tabulate your results

Sample Calculations from finding average mass of density bottle of saline solution (Refer to Appendix A for more):

\[\begin{gathered}\text{average} = \frac{\text{trial 1} + \text{trial 2} + \text{trial 3}}{3} \pm \frac{\text{range}}{2} \\ \text{So for 5 grams of salt;} \\ \frac{79.50+79.06+79.66}{3} \pm \frac{79.50-79.06}{2} = 79.07 \pm 0.30\end{gathered}\]

Sample Calculations for finding Density of saline solution for \(\mathbf{5g}\) of salt:
Empty density bottle (\(m_1\)) = 27.28 ± 0.01 g
Mass of density bottle with plain water (\(m_2\)) = 77.28 ± 0.01 g
Mass of plain water = \(m_2-m_1\) = 77.28 ± 0.01 g - 27.28 ± 0.01 g = 50 ± 2%
Volume of the bottle = \(\frac{m_{h_2,0}}{\text{density of water}} = \frac{50}{1}\) so volume of the bottle is 50 ± 2%
Mass of solution = \(m_3-m_1\) = 79.07 ± 0.30 - 27.28 ± 0.01 = 51.79 ± 0.31

Density is \(\frac{\text{mass}}{\text{volume}}\), therefore \(\frac{m_3-m_1}{\text{volume of bottle}} = \frac{51.79 \pm 0.60\%}{50 \pm 2\%} = 1.04 \pm 2.60\%\)
Absolute uncertainty = \(\frac{\text{percentage uncertainty}}{100} \times\) data value = \(\frac{2.60}{100} \times 1.04 = 0.03\)

So Density with absolute uncertainty = 1.04 ± 0.03