To study Michelson’s Interferometer and determination of the wavelength of he-ne laser.

To study Michelson’s Interferometer and determination of the wavelength of he-ne laser.

1. AIM :- To study M ichelson’s I nterferometer and determination of the wavelength of he-ne laser. Submitted To : Dr. N eelu Mahajan Submitted By : Tania Singla (2345669)

2. What is Michelson’s Interferometer A Michelson interferometer is a device used to measure small displacements, refractive index changes, or small wavelength differences in optics. It was invented by Albert A. Michelson in the late 19th century and has since become a fundamental tool in optics and interferometry . The basic setup of a Michelson interferometer consists of a beam splitter, which divides a single light beam into two beams traveling along perpendicular paths.

3. Michelson’s Interferometer The interference pattern depends on the relative phase difference between the two beams, which in turn depends on factors such as the path length difference between the two arms of the interferometer and any phase changes induced by the medium through which the light travels. By measuring changes in the interference pattern, scientists can precisely determine small changes in these factors, making Michelson interferometers valuable tools in fields such as metrology, spectroscopy, and gravitational wave detection .

4. Where Michelson interferometer are being used ? Measurement of Small Displacements Detection of Refractive Index Changes Wavelength Measurement Frequency Metrology Gravitational Wave Detection Surface Profiling and Imaging

5. INTERFERENCE Where two or more waves superpose to form a resultant wave of greater, lower, or the same amplitude. It occurs when waves meet while traveling through the same medium, and their amplitudes combine according to the principle of superposition .

6. I nterference There are two types of interferences :- Constructive interference : : O ccurs when the peaks of two waves align with each other, resulting in a wave with greater amplitude . Destructive interference : : Destructive interference occurs when the peak of one wave aligns with the trough of another wave, resulting in a wave with lower amplitude or even complete cancellation.

7. Compensating Plate A compensating plate is a transparent optical element inserted into one of the arms of the interferometer to compensate for any differences in optical path length between the two arms. This optical path length difference can arise due to various factors such as differences in the refractive index of the medium, temperature variations, or imperfections in the optical components.

8. Helium-neon Laser In a Michelson interferometer setup, the HeNe laser beam is typically split by a beam splitter, with one portion of the beam traveling along one arm of the interferometer and the other portion traveling along the other arm. After reflecting off mirrors at the ends of each arm, the beams recombine at the beam splitter, and interference occurs.

9. Apparatus required:-

10. mirrors Glass plates

11. Circular scale Convex lens

12. Working Principle:- INTERFERENCE . A beam of light from an extended source is divided into two parts of equal intensities by partial reflection and refraction . These beams travel in two mutually far directions and come together after reflection from plane mirrors . The beams overlap on each other and produce interference fringes.

13. Finding the wavelength . Here, we see our central fringe is dark. So, wavelength of the central dark fringe is : = ; where λ is the wavelength of the beam(in nm) d is the distance of mirror displaced (in mm) and n is the number of fringes. (Here we took n=100). Theoretical value of wavelength of He-Ne Laser is 632.8nm . So, experimental value should be around this value with less than 10% error.  

14. We O bserved

15. Observations Least count of main scale = 0.1 mm = 0.01 cm Least count of circular scale = 0.0001 mm = 0.0001 cm S . No. No. Of Fringes M.S.R ( cm ) C.S.R ( cm ) T.S.R ( cm ) Difference ( cm ) 1 100 0.065 0.00041 0.06541 0.00314 0.0032 2 100 0.062 0.00027 0.06227 3 100 0.059 0.00007 0.05907

16. Mean of Difference = = 0.00317 cm Wavelength = = = = 634 nm % error = = 0.18%   Calculations

17. Applications of Michelson’s interferometer:- The Michelson interferometer and its modifications are used in the optical industry  for testing lenses and prisms, for measuring index of refraction, and for examining minute details of surfaces Fourier transform spectrometer. Laser unequal path interferometer. Stellar measurements. Gravitational wave detection.

18. THANK YOU