Fabry perot etalon

to find separation distance

1. FABRY PEROT ETALON

2. Outline of the experiment : Aim of the experiment Introduction Theory Experimental set up Data Graphs Result Precautions Conclusion

3. Aim of the experiment To determine the separation between the plates of Fabry Perot etalon .

4. INTRODUCTION Charles Fabry and Alfred Perot designed Fabry Perot Interferometer in 1899 . A Fabry Perot Etalon or simply Fabry Perot Interferometer in which the distance between the two mirrors is kept fixed. It represents significant improvement over the Michelson interferometer . If the gap between Etalon mirrors is varied moving one of the mirror , the instrument is called Inteferometer . I f the mirrors are held fixed and adjustment screw are provided for parallelism then it is called Etalon. The multiple reflections of light rays inside the partially reflecting mirrors strengthen the constructive and destructive interference of the transmitted light resulting in much sharper rings compared to Michelson inteferometer .

5. Principle: The main principle of Fabry Perot Etalon is light is passed through a pair Of parallel , highly reflecting etalon. Interference between components of light undergoing multiple reflections result in extremely well defined inference fringes .

6. Theory: Let us consider a monochromatic light illuminating on etalon . A ray of light incident on M1 gets reflected and transmitted. The reflected ray continuous to get reflected inside the parallel reflecting surfaces , and some of the rays will be transmitted .The transmitted lights are collected on a screen and rings are observed. It makes use of multiple reflection which follow interference of thin films due to transmitted light.

7. Interference condition in Fabry Perot Etalon Consider two reflecting surfaces M 1 and M 2 seperated by a distance ‘d’ . Monochromatic light of wavelength ‘ λ ’ is being incident on M 1 making an angle ‘ Ө ’ With the normal. The ray incident at A gets partly reflected and partly transmitted . The transmitted ray A gets reflected at A 1 and some rays are transmitted i.e, E 1 . In the Similar way process of multiple reflection goes on. optical path difference is given by ( A 1 A 2 )+(A 2 B)=P From fig., cos2 Ө =A 2 B/A 1 A 2 A 2 B=A 1 A 2 COS2 Ө P=A 1 A 2 +A 1 A 2 COS2 Ө P=A 1 A 2 (1+COS2 Ө ) =2A 1 A 2 COS 2 Ө =2dCOS Ө [d=A 1 A 2 COS Ө ] If µ is the refractive index of the medium between Etalon the P=2µdCOS Ө

8. If the distance travelled inside by the rays becomes equal to integral multiple of wave length , maximum light gets transmitted inside mirrors and we observe constructive interference on screen. n λ =2µdcos Ө where n=0,1,2,3,4……….. If the distance travelled inside equals to (2n+1) λ then we observe dark bands due to destructive interference. (2n+1) λ =2µdcos Ө where n= 0,1,2,3,4………. FORMULA USED: n λ =2µdcos Ө Where λ =Wave length of light used Ө =Angle of incidence n=Order of interference d=separation between the plates µ=Refractive index between the plates Fig showing concentric rings

9. Experimental set up Laser Etalon Optical bench lens Scale given on a milky Transparent plastic plate

10. Procedure 1.With all the components perfectly set as given in previous fig, we can find a series of very intense concentric circular interference fringes on the screen. 2.Take the reading of the first bright ring on the left side ‘a’ . Repeat above procedure for 2,3,…6 fringes . Now take the readings on the right side of the fringes ‘b’ and repeat foe different no.of fringes. 3.Difference between a and b gives Angular diameter 2 Ө n. 4.Calculate Ө n and cos Ө n and tabulate the results in tabular column. 5.Draw a graph with order of interference on X-axis and cos Ө n on Y-axis. 6.Find the slope of the graph calculate the separation between the plates of etalon.

11. Ring number Angula r diameter b-a =2 Ө n Өn cos Ө n left(a) right(b) 1 2 3 4 5 6 7 5.9 5.3 5.1 4.9 4.6 4.4 4.3 6.1 7.2 7.7 8.2 8.4 8.6 8.8 0.2 1.9 2.6 3.3 3.8 4.2 4.5 0.1 0.95 1.3 1.65 1.9 2.1 2.25 0.99999 0.99986 0.99974 0.99959 0.99945 0.99933 0.99922 Distance between the screen and etalon is 50cm Tabular column

12. Distance between screen and etalon is 50cm

13. Ring number Angular diameter b-a=2 Ө n Ө n cos Ө n Left Right 1 2 3 4 5 6 5.1 4.7 4.5 4.3 4.1 4.0 6.3 6.7 7.0 7.2 7.4 7.5 1.2 2.0 2.5 2.9 3.3 3.5 0.6 1.0 1.25 1.45 1.65 1.75 0.9999451 0.9998476 0.9999762 0.9996797 0.9995853 0.9995336 Distance between screen and etalon is 45cm

14. Distance between screen and etalon is 45cm

15. CALCULATION Formula used is n λ=2dcos Ө n d=n λ /2cos Ө n d=( λ /2)(1/slope) [slope=n/cos Ө n] If distance between screen and etalon is 50cm d=(532*10 -9 )/(2*1.30714*10 -4 ) d=203.4977*10 -5 d=2.03497mm If the distance between screen and etalon is 45cm d=(532*10 -9 )/(2*8.3428*10 -5 ) d=3.18mm

16. Precautions 1.Do not touch or contact in any way either the front or back surfaces of the mirror pieces . Doing so will permanently damage the mirror coatings. 2. Avoid eye exposure to the direct laser beam. 3.While taking readings Etalon should remain stable, for this it can be fixed on the rectangular plate.

17. Result and conclusion Separation the plates of Fabry Perot etalon When distance between screen and etalon 50cm=2.03497mm When distance between screen and etalon 45cm=3.188mm Though the distance between the screen and etalon is varied t he separation between the plates remains constant as both t he etalon plates are fixed.