# Doppler Effect And The Fiber Gyroscope

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Contents

## Introduction

In this science experiment, we will measure rotation in a gyroscope using the doppler effect. Using the Sagnac interferometer, we will measure the frequency shift introduced by the doppler effect on a beam.

To perform this experiment, we will take rotation speed (number of turns per second) as our independent variable and the number of fringe shifts as our dependent variable. And we will be using a turntable as our rotating platform.

## Aim

To measure the rotation in a gyroscope using the doppler effect.

## Theory

1. The change in frequency of a wave with respect to an observer who is moving toward the frequency or away from it. It is termed Doppler Shift or Doppler Effect. The Formula for the Doppler effect is: 2. A device used for maintaining and measuring angular velocity and orientation is called a gyroscope. Gyroscope

3. A Sagnac interferometer is a device in which two mirrors and a beam splitter are arranged in a triangle. Sagnac Interferometer

## Requirements

1. Helium-Neon Laser

2. Sagnac Interferometer

3. Turntable

4. Beamsplitter

5. Notebook

## Procedure

Step 1: To assemble a Sagnac Interferometer, use a Helium-Neon laser. Where, on a rotating frame, two beams propagate in opposite directions. A long fiber will work as a beam carrier for both the propagating beams to produce the Doppler effect.

Step 2: Using a turntable is a rotating frame.

Step 3: Use a beam splitter to produce counter-propagating beams. These beams will be injected into the fiber.

Step 4: Obtain a fringe pattern on a screen created by returning the beam.

Step 5: Rotate the fiber on the turntable.

Step 6: Observe the change in the pattern of fringes.

Step 7: Observe the pattern of fringe by rotating it at three different speeds of 17, 33, and 45 rotations per minute.

## Observation

1. Our experiment performed the same as we expected it to perform.

2. We were successful in building the Fiber Optic Gyroscope. And we also measured the Doppler shift introduced by the rotating frame.

3. Our result came under five percent of accuracy.

## Result

1. The simple fiber optic gyroscope that we constructed in this experiment measured rotation with an accuracy of five percent. There are two reasons for this performance, the first one is the poor contrast ratio between fringes, and the second one is we counted fringes’ shifts with limited accuracy.

2. We used non-polarising material as fiber which is a reason for the poor contrast.

3. Another reason for poor contrast is facing difficulties in balancing the intensities of two beams.

4. This problem can be solved by repeating the experiment with the same speed at least ten times.

5. By repeating each experiment, we can successfully reduce the standard deviation by ten percent of the average value at a speed of 45 rotations per minute and forty-five percent of the average value at a speed of twenty-five rotations per minute

## Precaution

1. Repeat the experiment ten times with each speed.

2. Make sure every instrument is working properly.

## Conclusion

In this experiment, we measure the rotational speed using the doppler effect in a fiber-optic gyroscope.

Q.1 What was the aim of your experiment?

ANS. We aimed to measure the rotation in a gyroscope using the Doppler Effect.

Q.2 How much accuracy has the fiber gyroscope shown?

ANS. It measures rotation with five percent of accuracy.

Q.3 What is the reason behind the less accuracy?

ANS. They respond to it. First, we used non-polarising material as fiber, and second, we counted fringe shifts with limited accuracy.

Q.4 How can you solve the accuracy problem?

ANS. We can solve this problem by repeating each experiment ten times.

Q.5 The Sagnac Interference was named after which physicist?

ANS. Georges Sagnac.