Practice IA: What is the refractive index of Perspex determined by changing the incidence angle of a beam of light, resulting in a change of the measured refraction angle?

By altering the angle at which a light beam contacts a surface, and altering the recorded refraction angle, what is the refractive index of Perspex?

The report aims to ascertain Perspex's refractive index, a well-liked glass substitute. This is accomplished by projecting a light beam into a block of Perspex at various incidence angles (°), which produce various refraction angles. Perspex has numerous advantages over glass, which has a comparable refractive index (1.52), so I believed it was crucial to ascertain this material's refractive index. Perspex offers several advantages over glass that glass does not. Its 10% higher light transmission, 17 times greater strength than glass, improved durability, and lower density make it perfect for lightweight applications (Advantages of Perspex, 2018). Perspex is employed in practical applications such as aquariums, aquarium windows, and military applications because of these advantages. Refraction is a notion applied in many aspects of daily life, including vision. An image is focused onto the retina for a human to see and perceive by the refraction of light in the eye.

It is necessary to define a few essential notions before understanding the topics of this paper. These include the idea of refraction, knowledge of the characteristics of light, and comprehension of how various media affect light manipulation.

Diagram 1 illustrates how refraction occurs as light travels through one medium and then through another, changing its speed and, consequently, its wavelength and direction. However, refraction does not alter the frequency of the wave that constitutes light. Air, water, and in this case, Perspex are examples of mediums—substances that can transmit light—through which light can travel.

When a ray of light is shone from a medium of low density to high density, at an angle of incidence measured as the angle between the ray and an imaginary perpendicular ‘normal’ line, it refracts by a certain angle in the 2^nd medium. The beam is slowed, which causes the angle—known as the refraction angle—to bend in the direction of the normal line.

• Lightbox
• Power Supply – 12V
• Protractor - analog ± 2°
• Perspex block – 7.5cm × 5cm
• Pencil • Ruler – To draw lines
• A4 sheet of paper

As the thickness of the beam was a significant component that affected the readings of all angles in the experiment, a tool error of ±2° was transmitted as the error for the protractor. I determined that ±2° would be suitable because it was significant enough to consider my mistake in determining the location of the dispersed beam's centre. Additionally, it would enable the proper error bars to be shown on the graph.

The various angles of incidence, expressed in degrees, at which the light ray is directed toward the Perspex block during this experiment—more particularly, at 10, 20, 30, 40, 50, 60, 70, and 80°—are the independent variables.

The angles of refraction that the light ray produces as it travels through the Perspex block at various incidence angles serve as the experiment's dependent variable.

The level of light pollution present in the room when the experiment was conducted is the most important qualitative finding I made. This led to situations where drawing the line of refraction was difficult since it was difficult to see where the beam emerged from the Perspex block. The issue was soon resolved by turning off the room's lights, which made the space darker and made it simpler to see the flimsy beam of light that emerged through the Perspex block. The noticeable thickening and fading of the light beam that emerged from the Perspex was another thing that was noticed. This might result from dispersion, in which the single beam of light was split into several thicker, lower-intensity beams, giving the appearance of greater darkness. However, it made it extremely challenging to locate the developing beam's core.

Table 1: Raw Data

Processed Data Table 1

To examine the accuracy of the computed Refractive index of Perspex and its uncertainty, the relative error was calculated.

Relative Error in Experimental Refractive index of Perspex

\(Relative\,error \%=\frac{Absolute\ Uncertainty}{Absolute\ Value}×100%\)​​​​​​​

\(=\frac{0.19}{1.42}×100\%\)

\(=13.38\%\)

With the experimental refractive index of Perspex estimated as 1.42 ± 0.19, the experiment's goal of finding the material's refractive index by adjusting the incidence angle has been accomplished. Only 13.38% relative error suggests moderately high precision, which supports an effective experimental design.

Graph 2's linear trendline has an R² value of 0.99 and shows the relationship between sin(r) and sin(i). The R² number represents the percentage of variation in the dependent variable, in this case, the sine of the refraction angle, that can be accounted for by the sine of the incidence angle, the independent variable. It is scaled on a scale from 0 to 1, with 1 being the strongest correlation between the variables, and it indicates the strength of the association between these two variables (Andrew Bloomenthal, 2020). The R² score of 0.99 for this data set indicates that the variance of the various incidence angles accounts for 99% of the variation in the refraction angle, accurately fitting the trend line.

The experimental value of the refraction index of Perspex determined to be 1.42 ± 0.19 lies between the two values of 1.23 and 1.61. This experimental value increases the experiment's validity as the literature value of the refractive index of Perspex, 1.49, is present within the boundaries of the experimental refractive index. Therefore, the experimental value is validated by the literature value.

The precise correctness of this experimental value was determined using the calculation below.

\(\frac{theoretical \ value-expeimental \ value}{theoretical \ value}×100\)​​​​​​​

\(\frac{1.49\ -\ 1.42}{1.49}×100\)

\(4.70\%\)

This value demonstrates a 4.70% discrepancy between the experimental refractive index and the Perspex refractive index reported in the literature. With this level of accuracy only deviating by 4.70% from the literature value, it demonstrates that there is even less systematic error, strengthening the validity of the experimental method.

This experiment's precision and low mistake rates can be considered a strength. Given that the calculated refractive index of Perspex only differed by 4.70 percent from the value reported in the literature, it can be concluded that the experimental approach is very accurate. It implies that the purity of the Perspex block utilized, rather than impure or another plastic substitute for this material, is extremely indicative of Perspex. The fact that only one researcher conducted the measurements is a slight plus. By doing this, the restriction and chance that different researchers would interpret the findings differently, introduce more parallax errors, or reach different conclusions are removed. Due to the fact that these restrictions are automatically overcome by just one researcher, it marginally improves the experiment's precision.

Additionally, some constraints prevented a smaller error of 4.70% from being attained. This also applies to optical effects like dispersion. The ray of light that emerged from the Perspex block was significantly thicker than the ray of light that was incident. This is because dispersion made it difficult to determine the precise location of the light ray's centre, which had a significant impact on measurements of the angles of refraction. The tiny error in the final experimental refractive index could have been caused by this constraint, which was not considered.

The presumption that the light's wavelength will remain consistent throughout the trials is another restriction. This is inaccurate because the white light used in the experiment has a wavelength range of 400–700 nm, a wide range for the wavelength to vary throughout the experiment (Andrew Zimmerman Jones, 2006). As stated in the controlled variables for wavelength, this aspect of light has a significant impact on the refraction angle, which could lead to differing data with various wavelengths for various incidence angles. The experiment's validity is lowered as a result.

Conducting the experiment in a closed, dark room with no outside lights affecting the experiment is one improvement that might be done to strengthen the experiment's validity. The experiment was conducted in a bright room with many windows, which could have influenced how well the light box's beam blended with the surrounding lighting. It would be simpler to see the beam's location and to locate its centre as it emerges from the Perspex block if the experiment were carried out in a dark environment. Another method to increase the experiment's accuracy is to employ lasers as a single light source rather than the lightbox's existing source of diffracted light bulbs. This eliminates a lot of factors, including wavelength discrepancies (because lasers only have one wavelength) and the issue with light dispersion when it leaves the Perspex block. This enables more precise readings since the laser will disperse considerably less than the light beam emanating from the lightbox's slit.

It is abundantly clear from the experiment results that the research topic has been resolved. What can be done to adjust the incidence angle of a light beam so that the measured refraction angle changes? Different refraction angles were determined as a consequence of the experimental procedure, which involved shining a beam of light through a Perspex block from the air medium at various incidence angles ranging from 10° to 80°. By means of Snell's Law

\(\frac{n_1}{n_2}=\frac{sin\theta_r}{sin\theta_i}\)​​​​​​​

and its linearisation,

\(sin\theta_r=\frac{n_1}{n_2}\times sin\theta_i\)​​​​​​​

The inverse of the gradient of the trendline drawn with the processed data was used to determine the refractive index of Perspex.

\(sin\theta_r=0.705\times sin\theta_i-0.0113\)

From the published value of 1.49, the refractive index of Perspex was estimated to be 1.42 0.19 with a 95.3% accuracy. The experiment's success is attributed to the fact that the error in gradient, which indicates the accuracy of the refractive index and the error in the y-intercept, which indicates the systematic error in the experiment, are quite small. The determined refractive index was calculated with a relative error of only 13.38%, and it contained the literature value of 1.49 within its bounds. This is further reinforced by graph 2's R^{​​​​​​​2} value of 0.99, which demonstrates the strength of the relationship between the incidence angle and refraction angle. With all of this information, the experiment was successful in determining a Perspex block's refractive index. The experiment has also backed up my claim that Perspex can be used as a butter substitute for glass because glass's refractive index, 1.52, falls within the experimental range of 1.42 0.19, demonstrating the similarity in optical refraction between the two materials. With that, it can be said that the experiment was a huge success.