What am I doing wrong when applying boundary conditions in this E&M problem? Thanks for contributing an answer to Physics Stack Exchange! What kind of overshoes can I use with a large touring SPD cycling shoe such as the Giro Rumble VR? Anti-reflective coatings are used in a wide variety of applications where light passes through an optical surface, and low loss or low reflection is desired. [(thickness * n * 2∏) / λ] - ([(3 * thickness * n * 2∏) / λ] + ∏) = 2k∏ ? Anti-reflective coating effect on total internal reflection? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. You don’t need to worry about the boundary conditions. Cutting out most sink cabinet back panel to access utilities. Actually, I'd probably want to switch the two around to get a positive phase change, right? Could you guys recommend a book or lecture notes that is easy to understand about time series? EM Wave Reflection and Transmission Between with Anti-Reflective Coating, “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…. No need to calculate with the phase change in the glass. I am taking the wave to be travelling along the z-axis, with the coating and material on the xy-plane. $$\tilde {\vec E_{R_2}} +\tilde {\vec E_{R_3}} =\tilde {\vec E_{T_3}}$$ At this point it seems like I have more variables than I can solve for with my equations, and thats not even including the magnetic field analysis. Use MathJax to format equations. Regardless here it is. $$B^{\perp}_1= B^{\perp}_2$$ The idea behind anti-reflection coatings is that the creation of a double interface by means of a thin film gives you two reflected waves. rev 2020.11.24.38066, The best answers are voted up and rise to the top, Physics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, $$\epsilon_1 E^{\perp}_1= \epsilon_2 E^{\perp}_2$$, $$\vec E^{\parallel}_1= \vec E^{\parallel}_2$$, $$\frac 1 {\mu} \vec B^{\parallel}_1=\frac 1 {\mu} \vec B^{\parallel}_2$$, $$ \tilde {\vec E_{R_1}} + \tilde {\vec E_{T_1}} = \tilde {\vec E_I}$$, $$\tilde {\vec E_{R_2}} +\tilde {\vec E_{T_2}} =\tilde {\vec E_{T_1}}$$, $$\tilde {\vec E_{R_2}} +\tilde {\vec E_{R_3}} =\tilde {\vec E_{T_3}}$$. This would then generate expressions for reflected and transmitted waves in the coating (to keep it shorter I'll only show the electric field related expressions): $\tilde {\vec E_{R_1}} (z,t) = \tilde E_{0_{R_1}} e^{i(-k_1z- \omega t)} \hat x$, $\tilde {\vec E_{T_1}} (z,t) = \tilde E_{0_{T_1}} e^{i(k_2z- \omega t)} \hat x$, I can then apply the boundary conditions at the interface between air and the coating to relate the expressions: What if the P-Value is less than 0.05, but the test statistic is also less than the critical value? Now is where I start to struggle a bit. Simply use those coefficients (unless your instructor intends you to derive them from scratch here, which seems unlikely), and keep track of the phase accumulation within the dielectric slab. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. That’s how you derive the Fresnel reflection/transmission coefficients for an interface. How come an anti-reflective coating makes glass *more* transparent? Problem 2 A thin layer of anti-reflective coating with a thickness t - 745 nanometers (nm) and an index of refraction n-1.30 is placed on top of a glass surface with an index of refraction n=1.50. Except in the reflection coefficient, don’t take the absolute value. Once the wave reflects from the inner material I suppose I need to add another reflection and transmission between the coating and air media like so: Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Anti-reflective coatings can be … The anti-reflective coating consists of layers of metal oxides applied to the front and back of glass, plastic or polycarbonate lenses. For a better experience, please enable JavaScript in your browser before proceeding. Not physical result from the presence of surface charge density between dielectrics. Why are Stratolaunch's engines so far forward? Without bothersome reflections, more l… Homework Statement "A glass lens (n glass = 1.52) has an antireflection coating of MgF 2 (n = 1.38). $\tilde {\vec E_{T_1}}$ is then incident on the inner material of refractive index n, again reflecting and transmitting: $\tilde {\vec E_{R_2}} (z,t) = \tilde E_{0_{R_2}} e^{i(-k_2z- \omega t)} \hat x$, $\tilde {\vec E_{T_2}} (z,t) = \tilde E_{0_{T_2}} e^{i(k_3z- \omega t)} \hat x$, Boundary conditions can again be applied to relate expressions at the interface between the coating and the inner material: Study revealing the secret behind a key cellular process refutes biology textbooks, Irreversible hotter and drier climate over inner East Asia, Study of threatened desert tortoises offers new conservation strategy, Thin-Film Interference and Antireflective coating, Thickness of AntiReflection Coating for destructive interference, Spherical balloon with conductive coating, Frame of reference question: Car traveling at the equator, Find the supply voltage of a ladder circuit, Determining the starting position when dealing with an inclined launch. I think I must be overcomplicating the problem or missing some key simplification so I'd appreciate it if someone could give me some advice. Is the word ноябрь or its forms ever abbreviated in Russian language? Examples include anti-glare coatings on corrective lenses and camera lens elements, and antireflective coatings on solar cells. Is there a name for applying estimation at a lower level of aggregation, and is it necessarily problematic? Ok, I solved for part (a), and it makes sense.