Lab Report

Objective:

Understand the principles of diffraction and interference by conducting single slit and hair diffraction experiments using a 650 nm laser.

Materials:

• 650 nm red laser

• Arduino (for laser control)

• Single slit (of known width)

• Hair sample

• Screen

• Ruler

• Camera (for photographing diffraction pattern)

• ImageJ software (for analysis)

• Experimental stand

Part 1: Single-Slit Diffraction

1. Setup:

   • Mount the 650 nm laser on the experimental stand.

   • Connect the Arduino to power the laser.

   • Place the single slit in front of the laser beam.

   • Set the screen at a known distance from the slit (measure and record this distance).

2. Observation:

   • Turn on the laser and align it so the beam passes through the single slit.

   • Observe the diffraction pattern on the screen. Adjust the setup until a clear diffraction pattern (bright and dark fringes) is visible.

   • Measure the distance between adjacent dark fringes using a ruler and record the values.

3. Data Analysis:

   • Record the slit-to-screen distance D.

   • Use ImageJ to measure the fringe spacing y from the image of the diffraction pattern.

   • Calculate the slit width d using the formula:

1. • Compare the calculated slit width with the known value of the slit.

   • Repeat the experimental steps and use another

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Part 2: Hair Diffraction

1. Setup:

   • Place a hair sample on a sample slide and mount it in the laser’s path.

   • Ensure the laser beam passes directly over the hair.

   • Set the screen at a known distance from the hair.

2. Observation:

   • Observe the diffraction pattern on the screen.

   • If the pattern is unclear, adjust the alignment.

   • Measure and record the distance between adjacent dark fringes.

3. Data Analysis:

   • Use ImageJ to measure the fringe spacing y in the hair diffraction pattern.

   • Calculate the hair diameter d using the formula:

Compare your result with the average diameter of a human hair (~50 micrometers).

1. Concept Questions:

   • What is the fundamental difference between single slit diffraction and hair diffraction?

   • How does increasing the slit width affect the diffraction pattern?

   • Explain how the interference pattern changes with multiple slits compared to a single slit.

2. Data Interpretation:

   • If the distance between the slit/hair and the screen is doubled, what happens to the diffraction pattern? Explain using the formula.

   • Given the wavelength of light is halved (325 nm), what changes would you expect in the diffraction pattern for the same slit width?

Problems for Students:

 Problem 1: Single-Slit Diffraction Analysis

A 650 nm laser passes through a slit of unknown width. The screen is placed 1.5 m away from the slit. The distance between two adjacent dark fringes on the screen is 2.5 mm.

• (a) Calculate the width of the slit.

• (b) How would the fringe spacing change if the laser wavelength were changed to 500 nm?

 Problem 2: Hair Diffraction Calculation

In an experiment to measure a hair's diameter using a 650 nm laser, the screen is placed 1.2 meters from the hair. The distance between two adjacent dark fringes on the screen is 1.8 mm.

• (a) Calculate the diameter of the hair.

• (b) If the hair were twice as thick, what would happen to the fringe spacing?

 Problem 3: Comparison of Diffraction and Interference

A 650 nm laser is used to perform diffraction through both a single slit and a hair. The slit width is 30 micrometers, and the hair has a diameter of 50 micrometers. The screen is placed 1.0 meters away.

• (a) Calculate the fringe spacing for both the single slit and the hair diffraction patterns.

• (b) Compare the two results and explain differences in the diffraction patterns.

 Problem 4: Impact of Wavelength

In a single-slit diffraction experiment with a slit width of 40 micrometers and a screen distance of 1.0 meters, a student changes the laser wavelength from 650 nm to 450 nm.

• (a) How does the fringe spacing change with the new wavelength?

• (b) Explain the physical reasons behind this change.

 Problem 5: Practical Experiment Planning

You are tasked with designing an experiment to measure the diameter of a human hair using a laser. You can access a 650 nm laser, a sample slide, an Arduino setup, and a screen. Describe the steps you would take to ensure accurate measurements, including setup, data collection, and analysis.

• Include considerations for alignment, measuring tools, and error minimization.

1. Worksheet (40%): Completeness and accuracy of theory, calculations, and explanations.

2. Assignment (30%): Detailed report, correct use of formulas, analysis, and discussion of results.

3. Problem Set (30%): Correctness of solutions, step-by-step calculations, and proper explanation.

Each lab group should download the Lab Report Template and fill in the relevant information as you experiment. Each group member should answer the Worksheet, Assignment, and Problem individually. Since each lab group will turn in an electronic copy of the lab report, rename the lab report template file. The naming convention is:

[Short Experiment Number]-[Student ID].PDF

Submit the Lab Report in PDf format