Optics 2

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Michigan State University *

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Electrical Engineering

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Apr 26, 2024

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Optics Lab 2 Group 12 Abbie Schraeger, Johnny Rioux, Zahreef Kazi, Jane Schell, Jacqueline Connelly

Goal The objective of this lab is to investigate the inference of light through both single and double-slit diffraction. The concept of light diffraction is essential in the world of science and everyday life. By experimenting, we were able to explore and understand the differences present in changing distance and its effect on light diffraction of the laser. The independent variable is the distance between the screen and the diffractor. The dependent variable is the length from the center to the second-order dot. The control variables are the wavelength and the slit width. In this lab, we are measuring how the distance affects the length of the laser that is being run through a diffractor. We are calculating y (the length of dark spots) from the equations below: 𝑦 = ?λ𝐷 𝑎 Experimental Setup Figure 1. Experimental setup for single-slit and double-slit diffraction

Figure 2. Experimental setup for Part 2. Plan of Approach Part 1: Single-slit Diffraction 1. Obtain materials ( white paper, ruler, beam stop, diffracting device, track, laser, viewing screen) 2. Place the diffracting device in front of the laser and set it to 0.04 mm slit width. 3. Decrease the distance between the diffracting device and the viewing screen by 10 cm each time 4. Measure the center of the dark spot to the 2nd order each time the distance is changed to obtain the values for y. It is important to note that our ‘m’ equals 2. 5. Plot the distance (cm) and dark spot distance (cm) in curve.fit to obtain a graphical representation of our data Part 2: Using Hair for Single Slit 1. Tape a strand of hair to the diffraction device and place it in front of the laser, 50 cm from the paper. 2. Measure the center of the dark spot to the first order to solve for ‘a’ Part 3: Double Slit Diffraction 1. Use the same setup shown above, but swap out the single-slit diffraction device for the double-slit diffraction device. 2. Repeat steps 2-5 in Part 1 for the double-slit diffraction device.

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Measurements Table 1. Measuring y from changing the distance from the single slit to the screen with a constant of a and wavelength when m=2. Wavelength D A Y when m=2 650 nm 100 0.1 cm ± 0.04 ± 0. 01 mm 3.4 0.1 cm ± 650 nm 90 0.1 cm ± 0.04 ± 0. 01 mm 3.2 0.1 cm ± 650 nm 80 0.1 cm ± 0.04 ± 0. 01 mm 2.7 0.1 cm ± 650 nm 70 0.1 cm ± 0.04 ± 0. 01 mm 2.3 0.1 cm ± 650 nm 60 0.1 cm ± 0.04 ± 0. 01 mm 2.0 0.1 cm ± 650 nm 50 0.1 cm ± 0.04 ± 0. 01 mm 1.7 0.1 cm ± Table 2. Measuring y from changing the distance from the double slit to the screen with a constant of a and wavelength when m=2. Wavelength D A Y when m=2 650 nm 100 0.1 cm ± 0.04 ± 0. 01 mm 4.0 0.1 cm ± 650 nm 90 0.1 cm ± 0.04 ± 0. 01 mm 3.4 0.1 cm ± 650 nm 80 0.1 cm ± 0.04 ± 0. 01 mm 2.9 0.1 cm ± 650 nm 70 0.1 cm ± 0.04 ± 0. 01 mm 2.7 0.1 cm ± 650 nm 60 0.1 cm ± 0.04 ± 0. 01 mm 2.3 0.1 cm ± 650 nm 50 0.1 cm ± 0.04 ± 0. 01 mm 1.8 0.1 cm ±

Evaluation of Uncertainty The uncertainty of our distance was the uncertainty of a ruler, which is 0.1 cm. The uncertainty for m is the same as that of distance because we used a ruler to measure this. The slit width ( 𝑎 ) was chosen by us as 0.04; However, this is a slider that was used from the single slit diffractor and with this we chose to give ourselves a 0.01 mm of uncertainty as we could have been closer to 0.03 or 0.05, but nothing greater than that as there were some landmarks on the slider. Data Analysis and Graphic Representation Results check for Part 1&3 λ/a ex) 650 nm → 0.00065 mm 0.00065 mm/0.04 mm= 0.01625= 1.625e-02 mm When m=2: 0.0325=3.25e-02 Slit width for Part 2 𝑦 = ?λ𝐷 𝑎 0. 5 𝑐? = 1(650??)(50 𝑐?) 𝑎 a=65000 nm

Figure 3. Graphical representation of the distance between the slit and screen (in cm) and the dark spot distance (in cm) when m=2 using single slit diffraction.

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Figure 4. Graphical representation of the distance between the double slit and screen (in cm) and the dark spot distance (in cm) when m=2 using double slit diffraction. Results and Evaluation In Part 1, as the distance decreases between the diffractor and the piece of paper where the laser is shown, the length of the dark spot decreases. Additionally, the laser became more clear and was easier to measure in centimeters as the distance decreased. Both our graph and our table show the y value when m=2. Our slope and lambda/a value match within our uncertainty, for both single-slit and double-slit diffraction. This allowed us to determine that our results make sense. For part 2, the slit width of a strand of hair came out to be 65000 nm. When converted this value is equal to 0.0065 cm, which is in the expected range of hair width. Both double and single-slit diffraction produced results of the dark spot decreasing when the distance between the laser diffractor and paper decreased. In double slit diffraction, there was a larger range of decrease between the dark spot length at 100 0.1 cm, which was 3.4 0.1 cm and at 50 ± ± ± 0.1 cm, which was 1.7 0.1 cm. These results produced a larger slope than our single slit ± diffraction, which were 4.0 0.1 cm at 100 0.1 cm, and 1.8 0.1 cm at 50 0.1 cm. The ± ± ± ± double-slit diffraction device naturally diffracts more light in comparison to the single-slit diffraction device. This is reflected in the experimental data we collected shown in the tables. Improvements

An improvement could be to make our measurements more precise by knowing exactly where the center of the 0 order dot is instead of estimating. This could be achieved by measuring from end to end of the center dot and then dividing by two, then placing the ruler at that distance. This would ensure that the center of the dot to the end of the 2nd order dot is properly measured. Another improvement that could be made is finding the y value when m=1 rather than when m=2. This would result in a decrease in uncertainty.