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Brewster's angle calculator

Find the incidence angle at which ideal p-polarized reflection vanishes for two transparent non-magnetic media.

Calculator

Brewster angle
56.3099
Refracted angle
33.6901

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How this calculator works

For lossless dielectrics, the reflected and refracted rays are perpendicular at Brewster incidence. The reflected beam then contains only the s-polarized component of initially unpolarized light. The simple index ratio assumes non-magnetic transparent media and a single flat boundary. Absorbing materials usually have a reflectance minimum rather than an exact zero.

Formula

tanθB = n2/n1; θt = 90 degrees - θB. Angles are measured from the surface normal.

Worked example

Light entering material of index 1.5 from air of index 1 has a Brewster angle of 56.310 degrees. Equal indices give 45 degrees, although their interface has no reflection at any angle.

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Frequently asked questions

Does all reflected light disappear?

Only the ideal p-polarized component vanishes. The s-polarized component can remain.

Is this the critical angle?

No. The critical angle marks total internal reflection and exists only when entering a lower-index medium.

Can I reverse the media?

Yes. The two Brewster angles are complementary for the same pair of transparent media.

Sources

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