Speed of Light: Rotating Mirror Experiment Examples

Introduction

Testing the speed of light has been a fundamental experiment in physics, particularly in the study of relativity. One of the classic methods employed is the rotating mirror experiment. This technique utilizes a rapidly spinning mirror to measure the time it takes light to travel to a distant point and back, allowing for a direct calculation of the speed of light. Below are three diverse examples demonstrating this method in practical contexts.

Example 1: The Classic Rotating Mirror Setup

Context

This is the foundational experiment originally proposed by Albert Michelson in the late 19th century. It serves as a benchmark for measuring the speed of light with high precision.

The experiment involves a light source, a rotating mirror, a beam splitter, and a distant stationary mirror. The light beam reflects off the rotating mirror and travels to the distant mirror, reflecting back to the rotating mirror, where it is detected.

Example

1. Equipment Needed:

   • Light source (such as a laser)
   • Rotating mirror
   • Beam splitter
   • Distant flat mirror (at least several meters away)
   • Detector (photodetector or photomultiplier tube)

2. Setup:

   • Position the light source and beam splitter so that the light beam is split into two paths: one towards the rotating mirror and the other towards the distant mirror.
   • Mount the rotating mirror on a precise motor, which allows for controlled rotational speed.
   • Ensure that the distance to the distant mirror is accurately measured.

3. Execution:

   • Start the rotating mirror at a known speed (e.g., 600 RPM).
   • Activate the light source, allowing the beam to travel to the distant mirror.
   • Measure the time it takes for the light to return to the rotating mirror. Due to the rotation, the angle of reflection will have changed, creating a measurable delay.

   • Use the formula:

     where c is the speed of light, d is the distance to the mirror, and t is the measured time difference, to calculate the speed of light.

Notes/Variations

• Adjust the rotational speed of the mirror to see how it affects the calculations.
• Use mirrors of different sizes to explore the impact on the accuracy of measurements.

Example 2: Rotating Mirror with Fiber Optics

Context

This variation incorporates fiber optics to enhance the precision of the speed measurement, allowing for more compact setups and reduced environmental interference.

Using fiber optic cables, the light can be guided to and from the rotating mirror, minimizing losses and external factors that could affect the speed measurement.

Example

1. Equipment Needed:

   • Laser light source
   • Rotating mirror
   • Beam splitter
   • Fiber optic cable
   • Distant mirror
   • Photodetector

2. Setup:

   • Connect the laser source to the input of the fiber optic cable.
   • Use the beam splitter to direct part of the light towards the rotating mirror while the other part is sent through the fiber optics to the distant mirror.
   • Ensure the fiber optic cable is securely fastened to prevent light loss.

3. Execution:

   • Initiate the rotating mirror at a predetermined speed.
   • Activate the laser to send light through the fiber optics to the distant mirror.
   • Measure the time for the light to travel to the distant mirror and back, accounting for the rotation of the mirror.
   • Apply the same speed formula to calculate the speed of light.

Notes/Variations

• Experiment with different lengths of fiber optic cables to determine their impact on measurement accuracy.
• Consider environmental factors such as temperature and pressure, which can affect light speed.

Example 3: Educational Demonstration in a Classroom

Context

This example focuses on a simplified version of the rotating mirror experiment suitable for educational purposes, allowing students to grasp the concept of light speed measurement through hands-on experience.

The setup is less complex but still illustrates the principles effectively.

Example

1. Equipment Needed:

   • LED light source
   • Hand-held rotating mirror (manual rotation)
   • Small flat mirror
   • Stopwatch
   • Measuring tape

2. Setup:

   • Place the LED light source on one end of the classroom and the small flat mirror at a measurable distance away (e.g., 10 meters).
   • Position the rotating mirror on a stand where it can be easily rotated by hand.

3. Execution:

   • Direct the LED beam towards the rotating mirror, then to the small mirror, and back to the rotating mirror.
   • Have a student rotate the mirror while another student uses a stopwatch to time how long it takes for the light to return.
   • Calculate the speed of light using the measured distance and time, employing the formula previously mentioned.

Notes/Variations

• Discuss the implications of the results and compare them with the known value of the speed of light.
• Encourage students to vary the distance and observe changes in the measurements.