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Brewsters Angle Formula

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Brewster's Angle is the angle of incidence at which the reflected light is completely plane polarized. Check FAQs

θ B = \arctan (\frac{n 1}{n ri})

θ_B - Brewster's Angle?n₁ - Refractive Index of Medium 1?n_ri - Refractive Index?

Brewsters Angle Example

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Here is how the Brewsters Angle equation looks like with Values.

Here is how the Brewsters Angle equation looks like with Units.

Here is how the Brewsters Angle equation looks like.

56.0463 = \arctan (\frac{1.5}{1.01})

56.0463° = \arctan (\frac{1.5}{1.01})

56.0463 = \arctan (\frac{1.5}{1.01})

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Brewsters Angle Solution

Follow our step by step solution on how to calculate Brewsters Angle?

FIRST Step Consider the formula

θ B = \arctan (\frac{n 1}{n ri})

Next Step Substitute values of Variables

∴

θ B = \arctan (\frac{1.5}{1.01})

Next Step Prepare to Evaluate

∴

θ B = \arctan (\frac{1.5}{1.01})

Next Step Evaluate

∴

θ B = 0.978192528724355rad

Next Step Convert to Output's Unit

∴

θ B = 56.0463034471456°

LAST Step Rounding Answer

∴

θ B = 56.0463°

Brewsters Angle Formula Elements

Variables

Functions

Brewster's Angle

Brewster's Angle is the angle of incidence at which the reflected light is completely plane polarized.

Symbol: θ_B

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Brewster's Angle

Refractive Index of Medium 1

Refractive Index of Medium 1 is the ratio of speed of light in vacuum to speed of light in medium 1.

Symbol: n₁

Measurement: NAUnit: Unitless

Note: Value should be between 1 to 3.

Formulas to find Refractive Index of Medium 1

Refractive Index

Refractive Index is a dimensionless quantity that describes how much light is slowed down or refracted when entering a medium compared to its speed in a vacuum.

Symbol: n_ri

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Refractive Index

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

ctan

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: ctan(Angle)

arctan

Inverse trigonometric functions are usually accompanied by the prefix - arc. Mathematically, we represent arctan or the inverse tangent function as tan-1 x or arctan(x).

Syntax: arctan(Number)

Other formulas in Devices with Optical Components category

Go Angle of Rotation of Plane of Polarization

θ = 1.8 \cdot B \cdot L m

Go Apex Angle

A = \tan (α)

Go Current Due to Optically Generated Carrier

i opt = q \cdot A pn \cdot g op \cdot (W + L dif + L p)

Go Diffraction using Fresnel-Kirchoff Formula

θ dif = a \sin (1.22 \cdot \frac{λ vis}{D})

How to Evaluate Brewsters Angle?

Brewsters Angle evaluator uses Brewster's Angle = arctan(Refractive Index of Medium 1/Refractive Index) to evaluate the Brewster's Angle, The Brewsters Angle formula is defined as the angle of incidence at which the reflected light is completely plane polarized also, the angle between the reflected and refracted ray is 90 degrees. It is given by arctan of the ratio of the refractive index of the medium in which the light ray is reflected to that of the incident ray. Brewster's Angle is denoted by θ_B symbol.

How to evaluate Brewsters Angle using this online evaluator? To use this online evaluator for Brewsters Angle, enter Refractive Index of Medium 1 (n₁) & Refractive Index (n_ri) and hit the calculate button.

FAQs on Brewsters Angle

What is the formula to find Brewsters Angle?

The formula of Brewsters Angle is expressed as Brewster's Angle = arctan(Refractive Index of Medium 1/Refractive Index). Here is an example- 3211.217 = arctan(1.5/1.01).

How to calculate Brewsters Angle?

With Refractive Index of Medium 1 (n₁) & Refractive Index (n_ri) we can find Brewsters Angle using the formula - Brewster's Angle = arctan(Refractive Index of Medium 1/Refractive Index). This formula also uses Tangent (tan)Cotangent (ctan), Inverse Tangent (arctan) function(s).

Can the Brewsters Angle be negative?

No, the Brewsters Angle, measured in Angle cannot be negative.

Which unit is used to measure Brewsters Angle?

Brewsters Angle is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Brewsters Angle can be measured.

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