Reflection and Refraction A short overview

Plane wave A plane wave can be written as follows: Here A represent the E or B fields, q=i,r,t and j=x,y,z So this is a representation of the waves that is valid i all three cases, i.e. the incoming, the reflected and the transmitted wave

Boundary conditions  For a wave moving from one medium to another medium we have:  (i)  (ii)

Boundary conditions  (iii)  (iv)

Form of E and B fields  Electric field and Magnetic fields are of the form;

Boundary conditions

Optical laws  All the three waves have the same frequency  Combined fields in medium (1) should be joined to the fields in medium (2)  Boundary conditions should hold at all times and at all points so exponential factors are equal. ………………………….

Optical laws  Spatial terms give when z = 0.  This holds if components are separately equal.If incident vector is in x-z plane, wave vector in y is zero.

Optical laws  The first law is 

Optical laws  Apply equation (1) to this equation (1.0) we get two results:   the optical laws apply to all waves  Reflection and Snell's law can in general apply to non- planar waves incident upon non-planar interface. This is shown below

Generalisation of the laws

REFLECTION AND REFRACTION  From boundary condition 2 above  From boundary condition(4)

Fresnel Equations  solve the two equations 

Continutation When  We get

Reflection and refraction At angle of incidence  E vector has no component in plane of incidence.  This makes it possible to get lineally polarized light from an unplarized beam. This fact is used in polarized sun glasses, the filter is oriented in such away that only light that is polarized vertically is transmitted, hence avoiding glare or annoying reflections from horizontal surfaces.

Total internal reflection  If we have 1 and at some point if  From Snell’s law we have  1  (transmitted ray glazes the surface.)

Total internal reflection  we have total internal reflection (no refracted ray at all). This phenomena is used in light pipes, fibre optics, and studying micro waves. In this case we have an evanescent wave which is rapidly attenuated and transports

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