Find the wave length of monochromatic light by using Michelson Interferometer
To find the wave length of Helium Neon LASER by using Michelson interferometer up to complete accuracyApparatus:
· Helium Neon LASER
· Michelson instrumental setup
· Focusing lens
· Meter rodMichelson Interferometer:
The Michelson interferometer was invented in1893 by Albert Michelson, to measure in SI units of the wavelength of the red line of the cadmium spectrum. With an optical interferometer, he measured distance directly in terms of wavelength of light used by counting the interference fringes. In the Michelson interferometer, coherent beams are obtained by splitting a beam of light that originates from a single source with a partially reflecting mirror called a beam splitter. The resulting reflected and transmitted waves are then reflected back by ordinary mirrors to a screen where they interfere to create fringes. This is known as interference by division of amplitude. Fig. 3.1
Interferometers are used to precisely measure the wavelength of optical beams through the creation of interference patterns.
Light is a transverse wave. When two waves of same wavelength and amplitude travel through same medium, their amplitudes combine. A wave of greater or lesser amplitude than the original will be the result. The addition of amplitudes due to superposition of two waves is called interference. If the crest of one wave meets with the trough of the other, the resultant intensity will be zero and the waves are said to interfere destructively. Alternatively, if the crest of one wave meets with the crest of the other, the resultant will be maximum intensity and the waves are said to interfere constructively.
In constructive interference, a bright fringe is obtained on the screen. For constructive interference to occur, the path difference between two beams must be an integral multiple of mλ of the wavelength λ,
Where m is the order, with
m =0, 1, 2, 3...
If the path difference between two waves is
the interference between them is destructive, and a dark fringe appears on the screen.
Light from a monochromatic source S is divided by a beam splitter (P′), (Fig.3.1) which is oriented at an angle approximately 45° to 50° to the beam, producing two beams of equal intensity. The transmitted beam (L) travels to mirror M1 and it is reflected back to P′. 50% of the returning beam is then reflected by the beam splitter and strikes the screen, D. The reflected beam (R) travels to mirror M2, where it is reflected. 50% of this beam passes straight through beam splitter and reaches the screen D.
Since the reflecting surface of the beam splitter P′ is partially reflecting surface, the light ray starting from the source S and undergoing reflection at the mirror M2 passes through the beam splitter three times, while the ray reflected at M1 travels through P′ only once. The optical path length through the glass plate depends on its index of refraction, which causes an optical path difference between the two beams. The recombined beams interfere and produce fringes at the screen D. The relative phase of the two beams determines whether the interference will be constructive or destructive. By adjusting the inclination of M1 and M2, one can produce circular fringes, straight-line fringes, or curved fringes.
The results shows that the actual wavelength of He-Ne LASER is greater than the calculated value, this error occurs due to in accuracy in measurements and due to apparatus error.
Percentage error =
Percentage error = 30.2%
The calculated results shows that the error in wavelength of red LASER is correct up to 68.8%.