Equipment required:

1. He-Ne laser source
2. Michelson interferometer apparatus
3. Beam splitter
4. Adjustable mirrors
5. Vacuum chamber (for refractive index measurement)
6. Pressure gauge
7. Ruler or micrometer for distance measurement

Theory

The Michelson interferometer is an optical device that splits a beam of light into two paths, reflects them back, and recombines them to create an interference pattern. By analyzing these patterns, precise measurements of the wavelength of light and the refractive index of air can be made. The interference fringes shift when the optical path difference between the two beams changes, allowing for the measurement of minute distances and wavelength calculations.

The Michelson Interferometer experiment is a crucial demonstration of the interference of light, instrumental in understanding both the wave nature of light and the precise measurement of physical properties. In this experiment, a beam of monochromatic light, such as from a He-Ne laser, is split into two beams using a beam splitter. These beams travel along different paths, are reflected by mirrors, and then recombine to produce an interference pattern of alternating bright and dark fringes. This pattern results from the constructive and destructive interference of the recombined light waves. During the procedure, the user can adjust the position of one of the mirrors, changing the path length of one beam, which shifts the interference fringes. By counting the number of fringes that move as the mirror is displaced, the wavelength of the light or small changes in distance can be measured with extreme precision. Additionally, this setup can be used to measure the refractive index of air by observing fringe shifts when air pressure or temperature is altered in one of the paths. In the first part, the wavelength of the He-Ne laser is determined by counting the movement of interference fringes as one of the mirrors is displaced. This movement is directly related to the wavelength of the laser light, enabling precise measurements. In the second part, the refractive index of air is measured by introducing a known change in air pressure or temperature in one of the interferometer’s arms. The resulting shift in the interference pattern provides the data needed to calculate how light's speed is affected by the medium, thus determining the refractive index of air.

Formula
λ = 2 * d/m

$$ \text{Refrective Index} = 1 + \frac{m*\lambda*p}{2*L*\Delta p} $$
          

• Cell length L = 7.056 cm
• Laser wavelength λ = 632.8 nm
• Atmospheric pressure p = 760 torr