when a uniform plane wave is incident obliquely (making an angle other than ) to the boundary between the two media then it is known as oblique incidence.

Now consider the situation that is more general case that is the oblique incidence.

In this case the EM wave (incident wave) not strikes normally the boundary. i.e, the incident wave is not propagating along any standard axes (like x,y and z).

Therefore EM wave is moving in a random direction then the general form is

it is also in the form .

then is called the wave number vector (or) the propagation vector.

and is called the position vector (from origin to any point on the plane of incidence) , then the magnitude of is related to according to the dispersion.

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i. and are mutually orthogonal.

ii. and lie on the plane .

then the field corresponding to field is .

Now choose oblique incidence of a uniform plane wave at a plane boundary.

the plane defined by the propagation vector and a unit normal vector to the boundary is called the plane of incidence.

the angle between and is the angle of incidence.

both the incident and reflected waves are in medium 1 while the transmitted wave is in medium 2 .

Now,

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the wave propagates

- .
- .
- .

(1) indicates that all waves are propagating with same frequency. (2) and (3) shows that the tangential components of propagation vectors be continuous.

implies since .

implies .

now velocity .

then from Snell’s law , where and are the refractive indices of the two media.