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What is the relationship between the angle of incidence and the reflected and transmitted light in Fresnel’s equations?

In Fresnel’s equations, the angle of incidence plays a key role in determining how much light is reflected and how much is transmitted when it strikes the boundary between two media.

As the angle of incidence changes, the proportions of reflected and transmitted light also change, and this relationship differs for s-polarized and p-polarized light.

For small angles of incidence:

  • Most of the light is transmitted into the second medium.
  • Only a small portion is reflected.

As the angle increases:

  • The amount of reflected light gradually increases.
  • The amount of transmitted light decreases.

For p-polarized light:

  • There is a special angle called the Brewster angle where no p-polarized light is reflected—it is all transmitted.
  • Beyond this angle, the reflected light increases again.

For s-polarized light:

  • Reflection increases steadily with angle and never reaches zero.
  • There is no Brewster angle for s-polarization.

At very high angles (close to 90 degrees):

  • Most of the light is reflected, and very little is transmitted.
  • If light travels from a denser to a rarer medium and exceeds the critical angle, total internal reflection occurs—no light is transmitted.

Thus, Fresnel’s equations show that the angle of incidence directly affects how much light is reflected or transmitted, and the effect depends on polarization and the materials involved.

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