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Brewster's Angle Calculator

Find Brewster angle where reflected and refracted rays are perpendicular

Parameters

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Show Trail

Controls

xⓘ

Calculated Values

Brewster's Angle:
33.69;°33.69;°

Examples

Glass to air

n₁=1.5, n₂=1.

    Visualization

    Brewster's Angle

    When unpolarized light reflects off a dielectric interface, reflected and refracted rays are usually partially polarized. At Brewster angle θB, reflected and refracted rays are perpendicular: tan θB = n₂/n₁.

    At θB, reflected light is completely plane-polarized perpendicular to the plane of incidence. This is used in polarizing filters and laser windows (Brewster plates).

    From Snell: n₁sinθB = n₂sinθᵣ and θB + θᵣ = 90° gives tanθB = n₂/n₁. Example: glass to air n₂/n₁ = 1/1.5 → θB ≈ 56.3°.

    Polarized sunglasses block horizontal glare (partially polarized reflection from roads/water). Brewster angle depends on coating and wavelength slightly.

    Distinct from critical angle: Brewster does not require n₁ > n₂, though both involve reflection at interfaces.

    Key Concepts

    • tan θB = n₂/n₁
    • Reflected ⊥ refracted at θB
    • Plane-polarized reflection
    • Polarizing sunglasses
    • Laser Brewster window

    Real-World Applications

    • Polarized sunglasses
    • Laser cavity windows
    • Reducing glare photography
    • Material index measurement
    • Class 12 polarization

    Explore Further

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    • Spherical Mirror Equation

      Calculate image position and magnification for concave and convex mirrors.

    • Lens Power

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    • Critical Angle

      Find critical angle for total internal reflection between two media.

    Physics Equations

    Brewster's Law:
    tan⁡θB=n2n1\tan\theta_B = \frac{n_2}{n_1}

    Step-by-Step Solution

    See how the main results are calculated.

    1

    Step 1: Brewster's Law

    Equation:

    tan⁡θB=n2n1\tan\theta_B = \frac{n_2}{n_1}

    Explanation:

    At θ_B, reflected and refracted rays are perpendicular.

    2

    Step 2: Indices

    Result:

    n1=1.5,n2=1n₁ = 1.5, n₂ = 1
    3

    Step 3: Angle

    Calculation:

    θB=arctan⁡(1/1.5)=33.6901°\theta_B = \arctan(1/1.5) = 33.6901°

    Result:

    θB=33.6901°θ_B = 33.6901°
    4

    Step 4: Polarization

    Reflected light is plane-polarized.

    Explanation:

    Brewster windows in lasers; sunglasses use polarization.

    5

    Step 5: Snell at Brewster

    Equation:

    n1sin⁡θB=n2cos⁡θBn_1\sin\theta_B = n_2\cos\theta_B

    Explanation:

    Follows from tan θ_B = n₂/n₁.

    6

    Step 6: Application

    Reduce glare from horizontal surfaces.

    Explanation:

    θ_B depends on interface materials.

    Frequently Asked Questions (FAQ)

    Always 100% polarized?

    Ideal dielectric at exact θB; real surfaces differ slightly.

    Measure n?

    Find θB where reflected light is fully polarized.

    Practice MCQs

    1. Brewster law:
    2. At θB reflected light is:
    3. θB + θᵣ equals:
    4. Glass to air θB about:
    5. Brewster vs critical angle:
    6. Polarizing glasses block:

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