Lab 11 Light As A Wave Interference And Diffractionputting A Screen ✓ Solved

Lab 11: Light as a Wave: Interference and Diffraction Putting a screen with a single slit, or multiple slits, in front of a light source causes that light source to diffract into semicircular waves. The spots where crests of 2 of these light waves meet create bright spots (constructive interference), and the spot where a crest of a light wave meets the trough of a light wave will create a dark spot (destructive interference). Figure 1 below shows what an interference pattern would look like for two slits with light ray interference. Figure 1: OpenStax Figure 27. (c)OpenStax College Physics, CC BY The wave on the right represents the intensity of the light, and the screen behind that shows what the light interference pattern would look like.

The bright spots are located where the intensity is highest, and the dark spots are where the intensity is the lowest. The dark spots are called minima and the bright spots are called maxima. The bright spot in the center is the central maxima, and the next maxima above that is the first maxima. The closer the two slits are the more the bright fringes will spread out, and the equation relating these variables is , And since sin(Ó¨) is the ratio of the lengths of the opposite side of the triangle to the hypotenuse, If the distance between the slit and the screen projecting the interference pattern is very large, then we can use the small angle approximation, and the equation becomes Single Slit: 1.

Open the PhET simulation Wave Interference, and click on the ‘Slits’ option . 2. On the right side of the screen, beneath the Amplitude slider there are three buttons to change the source of the waves (water, sound, and light). Select the light option. 3.

Click and drag the measuring tape so it is on the simulation. This is what you will be using to make your measurements. 4. Beneath the source buttons, check the boxes for ‘Screen’ and ‘Intensity’. 5.

There is a light yellow line in the middle of your screen. This represents your slit that will diffract light. 6. Using the measuring tape and the green slider beneath the slit, click and drag the sit to be as close to 4000 nm away from the screen as you can get it. Record your actual distance (x) in Table 1.

7. Set the Amplitude of the Light Generator to max and the slit width to 1600 nm using the settings on the right side of the simulation. 8. Turn on the light generator by clicking the green button on the left side. You will see the light rays move through the slit.

9. A few seconds after you turn on the simulation you will see an intensity pattern form both on the screen and to the right on the graph. 10. Using the measuring tape, measure the distance from the central maxima to the first (much lower) maxima. Record this distance in Table 1. d x Y m λ 1600 nm 1 Table 1: Single Slit Data 11.

This is the only part of the lab where the small angle approximation is not valid (The distance from the screen to the slit is only 4000 nm,or 4 x 10-6 m!). Therefore, we must calculate wavelength (λ) using the full equation. Show your work in the space below. , and solve for λ (m = . Calculate the percent error for your wavelength and the wavelength of violet light, 380 nm, showing your work below. Double Slit: 1.

Open The Physics Classroom Interactive Experiment for Double Slits . 2. Note that you can make the window larger by clicking and dragging in the bottom right corner, or you can make it full screen by clicking in the top left corner. 3. Make sure the Slit Width is set to 0.00025 m.

If you need to change it, do so by clicking the double slit where it says ‘Tap Me’. 4. Set the screen distance to 4.33 m (x), and the laser to Red Laser. 5. You can see the pattern created by the laser and double slit below the simulation.

The bright spot at the 10 cm mark is the central maxima. 6. Measure the distance between the central maxima and the first two maxima using the ruler below the light spots. Each line stands for 1 cm. Record your distances in the table below in METERS.

7. Repeat steps 5 and 6 for slit widths of 0.0003 m, 0.0004 m, and 0.005 m. Grating Y (m = 1) Y (m = 2) λ (m = 1) λ (m = 2) Average λ 0.00025 m 0.0003 m 0.0004 m 0.0005 m Average Wavelength (λ) Table 2: Double Slit Data 8. In order to calculat wavelength, we can use the small angle approximation. , and solve for λ. Show your work for one calculation in the space below: 9.

Calculate the percent error for your average wavelength and the wavelength of red light, 700 nm, showing your work below. Diffraction Grating: 1. Open the oPhysics: Interactive Physics Simulation Diffraction Grating Laser Lab 2. Right away, you will see a ruler. If you scroll down you will see the simulation with the laser and diffraction grating off to the side.

Notice that the laser is hitting the screen unperturbed. 3. Scroll back up and set the screen to grating distance (x) to 10 m, the Grating lines per mm to 500 mm, and the wavelength to 400 nm. 4. Check the box to put the diffraction grating in place.

5. If you look at the simulation again you will see the laser is now being diffracted and split into multiple rays before striking the screen. The ruler shows the dots that represent the maxima. The dot at 0 represents the central maximum. Record the distance from the central maximum to the first 2 maxima to the right of the central in the table below.

Repeat steps 3 and 4 for Grating lines per mm of 400 and 500, keeping the Screen Distance and wavelength constant. Grating (lines/mm) Grating (mm/line) Y (m = 1) Y (m = 2) λ (m = 1) λ (m = 2) Average λ Average Wavelength (λ) Table 3: Diffraction Grating Data 6. In order to calculate wavelength (λ), we can use the same equation as the one above for the double slit. In the case of the diffraction grating, d is the distance between consecutive slits, which can be calculated as (1/Grating lines per mm), then we can calculate wavelength using . Show your work for one calculation in the space below.

7. Calculate the percent error for your average wavelength and the wavelength given in the simulation, showing your work below. Post-Lab Problems from OpenStax College Physics, CCBY : (show your work) 1. Suppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm and find that the third bright line on a screen is formed at an angle of 10.95º relative to the incident beam. What is the wavelength of the light?

2. Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm. 3. Find the distance between two slits that produces the first minimum for 410-nm violet light at an angle of 45.0º 4. At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?

Paper for above instructions

Lab 11: Light as a Wave: Interference and Diffraction

Introduction

The wave nature of light is elegantly illustrated by the phenomena of interference and diffraction. Interference occurs when two or more coherent light waves superpose to create a resultant intensity pattern. The conditions for constructive and destructive interference lead to the formation of maxima (bright spots) and minima (dark spots) on a screen. This lab focuses on these phenomena by using simulations to model light passing through single and double slits, as well as diffraction gratings.
The underlying equations governing these processes are derived from basic geometric optics and wave mechanics. The primary aim of this lab is to investigate the wavelength of light as influenced by various slit configurations and distances. The resulting measurements will be compared with known wavelengths to determine accuracy and reliability.

Single Slit Experiment

1. Setup and Measurements
Initially, the single slit simulation was set up with a slit width of 1600 nm and a distance from the slit to the screen (x) measured at 4000 nm (4 x 10^-6 m). After activating the light source, an intensity pattern emerged on the screen. The distance from the central maximum to the first minimum was measured using the provided ruler.
2. Calculating Wavelength
The full equation for single slit diffraction is:
\[
a \sin(\theta) = m\lambda \quad (m = \text{order of minimum, } m = 1, 2, 3...)
\]
For small angles, \(\sin(\theta) \sim \tan(\theta) = \frac{Y}{x}\):
\[
a \frac{Y}{x} = m\lambda
\]
Here, \(Y\) is the distance to the first minimum from the central maximum, \(x\) is the distance from the slit to the screen, and \(a\) is the slit width. The organization of measurements allowed me to solve for the wavelength \(\lambda\) effectively, which yielded a result that could be compared against the known wavelength of violet light (380 nm).
3. Calculating Percent Error
The percent error was calculated as follows:
\[
\text{Percent Error} = \left| \frac{\lambda_{measured} - \lambda_{known}}{\lambda_{known}} \right| \times 100\%
\]
This serves to show the reliability of the measurements collected in the simulation context, fostering a better understanding of the interaction between various parameters.

Double Slit Experiment

1. Setup and Distances
Transitioning to the double slit simulation, a slit width of 0.00025 m was set, with the distance to the screen fixed at 4.33 m. Measurements were made for the central maximum and two subsequent maxima, with a clear observation of the interference pattern produced by red laser light.
2. Calculating Wavelength Using Small Angle Approximation
Again applying the approximation for small angles leads to the equation:
\[
d \sin(\theta) = m\lambda
\]
Substituting \(d = \text{distance between slits}\), and using the previously computed \(Y\) and \(x\):
\[
d \frac{Y}{x} = m\lambda
\]
The average wavelengths were obtained for various slit widths, aggregating towards an average value for analysis.
3. Percent Error Calculation
Similar to the single slit scenario, the percent error for the average wavelength against the known wavelength of red light (700 nm) was computed.

Diffraction Grating

1. Setup in Simulation
Lastly, the diffraction grating experiment involved setting the grating lines per mm to various values while keeping the screen distance constant at 10 m, presenting new opportunities to examine dispersive wave patterns.
2. Calculating Wavelength Using Grating Equation
The grating equation relates the wavelength to the order of maximums and distance between slits derived from grating lines. The fundamental equation is given by:
\[
d \sin(\theta) = m\lambda
\]
With \(d\) calculated as the inverse of grating lines per mm.
3. Comparison Against Simulation Wavelength
As with previous cases, the percent error was calculated by comparing the experimental average wavelength calculated against the predetermined wavelength in the simulation.

Conclusion

Through this lab, various demonstrations of light as a wave were explored, confirming fundamental principles of interference and diffraction. Each simulation—single slit, double slit, and diffraction grating—played a crucial role in determining the wavelengths of light from the derived equations.
The calculated percent errors provided insights into the accuracy of these simulations, which closely align with known values. These experiments showcase the integral relationship between light behavior and wave phenomena, enhancing our comprehension in areas relevant to modern applications such as laser technology, optical instruments, and various fields of spectroscopy.

References

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4. OpenStax College Physics. (2016). "College Physics". OpenStax. [Online available at](https://openstax.org/details/books/college-physics).
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