In this model of Michelson interferometer, sodium vapor lamp is used as light source. Sodium has two emission wavelengths that have extremely close values and without sensitive equipment, it cannot be distinguished. Measurement of these lines, designated as D1 and D2 Fraunhofer lines, the average wavelength as well as difference between the two emission lines of sodium can be determined. The purpose of this experiment is to measure the wavelength of Sodium D emission lines.
The two beams of a Michelson interferometer interfere constructively when the waves add in phase and destructively when they add out of phase, producing circular interference fringes as a result. From this we can calculate wavelength of sodium source. The interference pattern observed with the sodium lamp contains two sets of fringes which disappear when the bright bands of one set are superimposed on the dark bands of the other. The wavelength separation of the Na D-line doublet is easily determined by observing the successive coincidence and discordance of the two sets of fringe systems produced by the doublet of wavelengths (λ1 and λ2 with λ1 > λ2 ). As D is increased, the two systems gradually separate and the maximum discordance occurs when the rings of one system are set exactly halfway between those of the other system. The discordance positions are most clearly seen as minima in the contrast of the pattern.
Wavelength separation λ1 - λ2 = λ2 / 2D
where λ is the average wavelength of the sodium and D is the change in position of the micrometer for two successive discordance / coincidence.
The wavelength of laser is calculated by;
λ = (2d / N) Δ
where ‘d’ is the change in position that occurs for ‘N’ fringes to pass and Δ is the calibration constant of the micrometer
The light passes through a greater length of glass as the plate is rotated. The change in the path length of the light beam as the glass plate is rotated and relates the change in path length with the laser beam through air.
The refractive index of glass slide,
N = (2t - Nλ) (1- cos θ) / 2t (1-cos θ) - Nλ
Where t is the thickness of the glass slide, N is the number of fringes counted, λ is the wave length of light used and θ is the angle turned for N fringes.