Question

In thin film interference, an (a) incident wave reflects off of the front interface of the thin film and (b) refracts into the thin film.This refracted wave then (c) reflects off of the back interface of the thin film yet also (d) transmits through the film.This reflected wave then (e) refracts back through the front interface of the thin film in order to interfere with the wave that initially reflected off of the front interface.Apply the Fresnel equations that we derived in class along with Snell’s law to arrive at an expression for waves (a) through (e) above in terms of the index of refraction of the surrounding medium n1, the index of refraction of the thin film n2, the incident angle (?i), the thickness of the thin film d, and the wavelength of the incident light ?. Include a diagram of the light rays and give the expression for the path length through the thin film.

please write and indicate each part clearly

Answer 1

Thin film inter faxe PA thin wedge shaped fim bounded by the surfoce AB and CB haring Pefartve A index no enclou sed the Mi augle< which is ca tled as frx) R. Ledgo anglex. T2 Let pe ray of cwaselongih a be încident at an angle "?" on the wedge shoped fiim wshen PR incdent on & is partio ly Refiected along Q; and gets pantially xebractod along OR, The refrauctid ray oe a gai n get reflect d rom e avlong es and parn tiarly reba -ctod aulang ell Hence the incident angle is i and the rebractons angle at first suntace isY. Nouo the reftected ray Ps fom -the of the thin film co agoi n gets Suntare partiaily rettecbod along Sv and pan tra ly pontionly Yef le tod Scanned with CS CamScanneut atong meet worth the So can d

As a vesult ase have a set 1t retlected o So and another branch of hansmitted Tays RT, VTD - ete At each point Q,RS-etC t evch reftected, The vest etc au fraction of ight te that Co ands Only vefactad one reftection each have aimost the Same întensities the says 0o and Sö are denived from the Same încident vay saffering ond hence -they are and we Caun mutaally imtenfavce siter each othen to provide întert erence phenomenai Similaaly coherent the ays along RT cond VT. are also Cohere nt to each othen and hence on meeting they also prod u ce îintexfenence parttern at any another point 'o" Interface due to Refletid bec aule From -the picture it ĭS Clear that the So On superposiiờn twill ys Oo and so on supemposiưon cwill produco înterf erence due to yrefteebd boaves find the parth diffrence (oY ) tet as parth expression blw tîme successive Tays (le@o and so). and to compile Us first drauw SNIDO SNK ref te cid that let CS and sL ICD.

let as produce oe and SL TO meet aut M. The parth of the reflectid beams meat at M. The parth of the nohich aro goint to Loi l be equal from the dotted (they meet tine SN opto 0 are very clase to each othen) Nous pauth difence betweon the above caid intenfaring beams 4= pasthris (@R+Rs) H-ON Here H: nolni is the refractive înder of the thin film with respect to the medium (n) Sกามคลด 4: (RNI + MR+ RS)M- ON-0 Fom the geomehy in we have RS: RM and SL:LM : d, -the fiim thickness at s. Now applying Shells tao Sini ONfos ON/OS sinr ON Abw ea o becomes 4:(ONI+ N,R + RS) H- H(ON, (NIR+RS)H: H(NIR tRM) as RS2 RM CS A M·N, M

H [SNI LS(a-)] hom 4 SMM LS(?=«): Ni M SM NiM: SM Ls(Y-K) SM : SL+ LM 4: Q Hd LS (Y-x) Jn auddi tion to -this parth diftenence, thene abrupt extras phase difberene of t eaualent to a parth difberence of I A/2 coused refiection aut Q. from the by Surfar ce backed by denser medium as nzn) The refiection ot R from the suatace backed the rarer medium, iu not cause by any change of phose so în the vefle chd Systm the net paith difbereme blw the two reftectod Yays (00 and So) is given by of phose so în the reftecod Scanned with CamScanner CS

Here H: n2 The datio of refractive indices A: wedgo tilm winth Y= Yetractive augle at tirst rehaction - Duedge angle being the wave length of the given w monochromatic ight-