Why there is interference pattern?

[KFC]

I am reading something about electromagnetic wave. There is a semi-infinite medium with refractive index n>1 on z>0 region. For z<0 region, it is medium with refractive index n=1. Two EM waves starting to propogate at the origin of xy plane with same wavenumber but different direction. Both of them are making angle $$\alpha (\alpha<\pi/2)$$ with positive z-axis on xz plane (one wave travel on -xz plane, the other on +xz plane). The material told there is an interference in x-direction? But I don't see how this happen. How to find the interference pattern?

BTW, could you recommend some book contains related concept?

Thanks.

 

[Valerie Park]

To answer your question, you can use the concept of Huygens' principle. Huygens' principle states that each point on a wavefront acts as a source of secondary wavelets, which together form a new wavefront. If you consider the two EM waves propagating in different directions, the wavefronts of the two waves will interfere with each other at the interface between the two refractive indices (in this case z=0). Thus, you can use the Huygens' principle to model the interference pattern in the x-direction. As for books, I would recommend Fundamentals of Photonics by Saleh and Teich and Principles of Optics by Born and Wolf.

 

[astrokreng]

The interference pattern in this scenario is a result of the wave nature of electromagnetic radiation and the properties of the medium it is traveling through. When two waves with the same frequency but different directions intersect, they will interfere with each other. This interference can result in constructive interference, where the waves reinforce each other, or destructive interference, where they cancel each other out.

In this case, the medium with a refractive index of n>1 will cause the waves to travel at different speeds, which will affect the phase of the waves when they intersect. This phase difference can result in the interference pattern observed in the x-direction.

To find the interference pattern, you can use mathematical equations such as the superposition principle and the Fresnel equations. These will allow you to calculate the resulting amplitude and intensity of the waves at different points in space.

As for book recommendations, "Introduction to Electrodynamics" by David J. Griffiths and "Optics" by Eugene Hecht are both excellent resources for understanding electromagnetic waves and their behavior in different mediums.