Michelson Interferometer bsc 4th year right now

Experiment No. 4

Title: Determination of wavelength difference of sodium source using Michelson Interferometer

Aim:

To determine the difference in wavelengths (Δλ) between the D₁ and D₂ spectral lines of sodium using a Michelson Interferometer.

Apparatus Required:

• Michelson Interferometer

• Sodium vapor lamp

• Rotating micrometer screw

• Lens and optical bench

• Screen or eyepiece

• Scale for fringe counting

Theory:

A Michelson Interferometer produces interference fringes due to the superposition of light beams reflected from two mirrors. If the sodium light contains two closely spaced wavelengths (D₁ and D₂), then the resulting fringes show periodic fading and reappearing.

The wavelength difference is given by:

 

$$\Delta \lambda = \frac{\lambda^2}{2 \Delta x}$$

​

Where:

• $\lambda$

  = average wavelength of sodium (≈ 589.3 nm)

• $\Delta x$

  = distance between successive disappearances of fringes

Procedure:

1. Set up the Michelson interferometer with a sodium vapor lamp.

2. Adjust the mirrors to obtain sharp, clear interference fringes.

3. Slowly move the movable mirror using the micrometer screw.

4. Count the distance (∆x) between two successive disappearances of fringes.

5. Repeat the measurement multiple times for accuracy.

6. Use the formula to compute the difference in wavelengths of sodium lines.

Observation Table: