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Critical Angle Calculator

Find critical angle when light goes from denser to rarer medium

Parameters

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Controls

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Calculated Values

Critical Angle:
41.81;°41.81;°

Examples

Glass to air

n₁=1.5, n₂=1.

    Visualization

    Critical Angle and Total Internal Reflection

    When light travels from a denser medium (higher n) to a rarer medium (lower n), Snell's law n₁sinθᵢ = n₂sinθᵣ gives a maximum incident angle. At critical angle θc, refracted angle is 90°: sin θc = n₂/n₁ (requires n₁ > n₂).

    For θᵢ > θc, all light reflects — total internal reflection (TIR). No refracted ray exists. Optical fibers guide light by TIR in a high-index core surrounded by lower-index cladding.

    Example: glass n₁ = 1.5 to air n₂ = 1 → θc = arcsin(1/1.5) ≈ 41.8°. Diamond n ≈ 2.42 gives θc ≈ 24.4° to air, enhancing brilliance.

    Critical angle differs from Brewster angle (polarization). TIR is used in prisms, endoscopes, and telecommunication fibers.

    Phase change on reflection is important in thin-film optics but not in simple critical-angle calculations.

    Key Concepts

    • sin θc = n₂/n₁
    • n₁ > n₂ required
    • TIR for θᵢ > θc
    • Optical fiber guidance
    • Snell at θᵣ = 90°

    Real-World Applications

    • Fiber-optic communications
    • Diamond cutting brilliance
    • Periscope prisms
    • Rain sensors
    • Class 12 TIR numericals

    Explore Further

    More optics tools

    • Snell's Law

      Calculate refraction angles and analyze light behavior at media boundaries.

    • Magnification

      Calculate linear and angular magnification for optical systems.

    • Thin Lens Equation

      Find image distance and magnification using 1/f = 1/u + 1/v.

    • Spherical Mirror Equation

      Calculate image position and magnification for concave and convex mirrors.

    • Lens Power

      Convert focal length to diopters and combine thin lens powers.

    • Diffraction Grating

      Calculate diffraction angles using d sin θ = mλ.

    Physics Equations

    Critical Angle:
    sin⁡θc=n2n1\sin\theta_c = \frac{n_2}{n_1}

    Step-by-Step Solution

    See how the main results are calculated.

    1

    Step 1: Critical Angle Condition

    Equation:

    sin⁡θc=n2n1\sin\theta_c = \frac{n_2}{n_1}

    Explanation:

    Requires n₁ > n₂ (denser to rarer medium).

    2

    Step 2: Indices

    Result:

    n1=1.5,n2=1n₁ = 1.5, n₂ = 1
    3

    Step 3: Check

    TIR possible

    Explanation:

    From glass to air: n₁≈1.5, n₂=1.

    4

    Step 4: Calculate

    Calculation:

    θc=arcsin⁡(1/1.5)=41.8103°\theta_c = \arcsin(1/1.5) = 41.8103°

    Result:

    θc=41.8103°θ_c = 41.8103°
    5

    Step 5: Total Internal Reflection

    θᵢ > θ_c → no refracted ray

    Explanation:

    Used in optical fibers and diamond sparkle.

    6

    Step 6: Snell Link

    Equation:

    n1sin⁡θc=n2sin⁡90°n_1\sin\theta_c = n_2\sin 90°

    Explanation:

    Refracted angle = 90° at critical incidence.

    Frequently Asked Questions (FAQ)

    No critical angle?

    When n₁ ≤ n₂, refracted ray always exists.

    Energy in TIR?

    Ideal TIR reflects 100%; real interfaces have evanescent wave in rarer medium.

    Practice MCQs

    1. TIR requires:
    2. sin θc =
    3. Glass to air θc about:
    4. θᵢ > θc:
    5. Optical fiber uses:
    6. Critical angle in water to air (n_w≈1.33):

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