Phys 201 Lab 1

Phys 201 Lab Name: Paul Dolphyne Ackah Lab Partners: Keyra, Amos Introduction In this laboratory report, we explore the fascinating phenomenon of interference, which occurs when two or more light waves of the same frequency overlap in space. This effect is contingent on both the phases and amplitudes of the waves and cannot be comprehended solely through ray optics or the particle-like nature of light. Instead, it necessitates the explicit recognition of light's wave nature. Two light sources are deemed coherent when they emit light waves of identical frequency and maintain a constant phase relationship between them. The light emanating from such sources is referred to as coherent light. Conversely, light from sources like lightbulbs, candles, or stars is considered incoherent due to its lack of phase coherence. It's worth noting that light waves are transverse waves. To observe interference using light waves on a laboratory timescale, an additional condition must be met: the interfering waves must share the same polarization. This can be achieved by using radiation from two different parts of the same wavefront. Procedure In this experiment, we directed a laser beam, which emits coherent light, through a slit. The slit's dimensions were controlled using an aperture bracket. The laser beam was focused on the slit, positioned approximately 20 cm away, and then projected onto a viewing screen situated 80 cm from the slit. This resulted in the formation of a horizontal interference pattern. We made adjustments to the slit sizes as necessary, using both 0.16 mm and 0.08 mm wide slits. We also conducted similar experiments with double slits. In these trials, we used a single slit width of 0.04 mm, while the separation distance between the double slits, denoted as 'd,' was set to either 0.25 mm or 0.50 mm. To record and analyze our experimental data, we employed the PASCO Capstone application. Data Experiment 1: Single Slit a = 0.16mm m L (cm) R (cm) (R-L) / 2 (cm) Theoretical (cm) % error 1 .0731 .0792 .00305 0.325 cm 6.15% 2 .0698 .0827 .00645 0.650 cm 0.77% 3 .0671 .0860 .00945 0.975 cm 3.08% 4 .0628 .0895 .01335 1.300 cm 2.69%

Experiment 2: Single Slit a = 0.08mm m L (cm) R (cm) (R-L) / 2 (cm) Theoretical (cm) % error 1 .0703 .0827 .0062 0.650 cm 4.62% 2 .0633 .0894 .01305 1.300 cm 0.38% 3 .0567 .0957 .0195 1.950 cm 0% 4 .0509 .1008 .02495 2.600 cm 4.04% Experiment 3: Double Slit a = 0.04mm d = 0.25mm n L (cm) R (cm) (R-L) / 2 (cm) Theoretical (cm) % error 1 .0774 .0795 .00105 0.104 cm 0.96% 2 .0748 .0813 .00325 0.312 cm 4.17% 3 .0730 .0832 .0051 0.520 cm 1.92% 4 .0712 .0857 .00725 0.728 cm 0.41% Experiment 4: Double Slit a = 0.04mm d = 0.50mm n L (cm) R (cm) (R-L) / 2 (cm) Theoretical (cm) % error 1 .0754 .0805 .00255 0.052 cm 390% 2 .0703 .0826 .00615 0.156 cm 294% 3 .0690 .0905 .01075 0.260 cm 313% 4 .0671 .0953 .0141 0.364 cm 287% The calculations and error analysis were conducted on the (R-L)/2 values, with corresponding percent errors presented in the tables above. The (R-L)/2 values represent the midpoint between each pair of minima. Percent error was determined using the following formula:

Pre Lab Questions 5. Suppose you added to the single slit an identical slit a distance d=0.25mm away from the first. Draw the resulting interference pattern you might expect on the same screen. What happens when we increase the distance between slits? What happens in the limit that d becomes arbitrarily large?

Introducing an additional slit to create a double-slit interference pattern results in the emergence of brighter and closely spaced fringes. As the separation distance 'd' between the slits becomes exceedingly large, the gaps between these fringes become progressively narrower. This effect gives the appearance of a continuous and uninterrupted strip-like pattern. Conclusion In this laboratory investigation, we explored the intriguing phenomena of interference and diffraction in the context of visible light. When multiple light waves of the same frequency intersect, they engage in interference, leading to constructive or destructive outcomes determined by their relative phases and amplitudes. To ensure the validity of our experiment, we employed a coherent light source in the form of a laser, which emits waves with a consistent phase relationship and frequency. Our double-slit experiments were based on interference theory, which demonstrated that constructive interference occurs when the path difference between waves is a whole-number multiple of the wavelength (λ), while destructive interference arises when the path difference is a half-number multiple of λ. In our single-slit diffraction experiments, we applied Huygens' principle, treating each point within the slit as an individual point source. The results from our initial three experiments were predominantly accurate. However, in the fourth experiment, the results were notably inaccurate, possibly due to erratic movement of the linear translator.