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Ray Optics Critical Angle Formula

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Critical Angle is the angle of incidence beyond which rays of light passing through a denser medium to the surface of a less dense medium are no longer refracted but totally reflected. Check FAQs

θ = {\sin (\frac{η r}{η i})}^{- 1}

θ - Critical Angle?η_r - Refractive Index Releasing Medium?η_i - Refractive Index Incident Medium?

Ray Optics Critical Angle Example

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Here is how the Ray Optics Critical Angle equation looks like with Values.

Here is how the Ray Optics Critical Angle equation looks like with Units.

Here is how the Ray Optics Critical Angle equation looks like.

64.3487 = {\sin (\frac{1.23}{1.12})}^{- 1}

64.3487° = {\sin (\frac{1.23}{1.12})}^{- 1}

64.3487 = {\sin (\frac{1.23}{1.12})}^{- 1}

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Ray Optics Critical Angle Solution

Follow our step by step solution on how to calculate Ray Optics Critical Angle?

FIRST Step Consider the formula

θ = {\sin (\frac{η r}{η i})}^{- 1}

Next Step Substitute values of Variables

∴

θ = {\sin (\frac{1.23}{1.12})}^{- 1}

Next Step Prepare to Evaluate

∴

θ = {\sin (\frac{1.23}{1.12})}^{- 1}

Next Step Evaluate

∴

θ = 1.12309585858299rad

Next Step Convert to Output's Unit

∴

θ = 64.3486526854391°

LAST Step Rounding Answer

∴

θ = 64.3487°

Ray Optics Critical Angle Formula Elements

Variables

Functions

Critical Angle

Critical Angle is the angle of incidence beyond which rays of light passing through a denser medium to the surface of a less dense medium are no longer refracted but totally reflected.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Critical Angle

Refractive Index Releasing Medium

Refractive Index Releasing Medium refers to the ratio of the speed of light in a vacuum to the speed of light in the medium that the light ray is approaching the interface from.

Symbol: η_r

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Refractive Index Releasing Medium

Refractive Index Incident Medium

Refractive Index Incident Medium refers to the ratio of the speed of light in a vacuum to the speed of light in the medium that the light ray is incident on.

Symbol: η_i

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Refractive Index Incident Medium

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other formulas in Fiber Design Characteristics category

Go Numerical Aperture

NA = \sqrt{({η core}^{2}) - ({η clad}^{2})}

Go Refractive Index of Fiber Core

η core = \sqrt{{NA}^{2} + {η clad}^{2}}

Go Refractive Index of Cladding

η clad = \sqrt{{η core}^{2} - {NA}^{2}}

Go Normalized Frequency

V = \sqrt{2 \cdot N M}

How to Evaluate Ray Optics Critical Angle?

Ray Optics Critical Angle evaluator uses Critical Angle = sin(Refractive Index Releasing Medium/Refractive Index Incident Medium)^-1 to evaluate the Critical Angle, The Ray Optics Critical Angle formula is the angle of incidence at which a light ray traveling from a medium with a higher refractive index (ni) to a medium with a lower refractive index (nr) undergoes total internal reflection at the interface. It is a fundamental concept in optics that describes the boundary condition for light propagation between different media. Critical Angle is denoted by θ symbol.

How to evaluate Ray Optics Critical Angle using this online evaluator? To use this online evaluator for Ray Optics Critical Angle, enter Refractive Index Releasing Medium (η_r) & Refractive Index Incident Medium (η_i) and hit the calculate button.

FAQs on Ray Optics Critical Angle

What is the formula to find Ray Optics Critical Angle?

The formula of Ray Optics Critical Angle is expressed as Critical Angle = sin(Refractive Index Releasing Medium/Refractive Index Incident Medium)^-1. Here is an example- 3686.906 = sin(1.23/1.12)^-1.

How to calculate Ray Optics Critical Angle?

With Refractive Index Releasing Medium (η_r) & Refractive Index Incident Medium (η_i) we can find Ray Optics Critical Angle using the formula - Critical Angle = sin(Refractive Index Releasing Medium/Refractive Index Incident Medium)^-1. This formula also uses Sine (sin) function(s).

Can the Ray Optics Critical Angle be negative?

No, the Ray Optics Critical Angle, measured in Angle cannot be negative.

Which unit is used to measure Ray Optics Critical Angle?

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

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