Refracted Angle using Snell's Law Calculator

✖Refractive Index of Medium 1 represents the ratio of the speed of light in a vacuum to the speed of light in medium 1. It quantifies the optical density of the medium.ⓘ Refractive Index of Medium 1 [n₁]			+10% -10%
✖The incident angle refers to the angle between the impact direction and the solid surface. For a vertical impact, this angle is 90 degrees.ⓘ Incident Angle [θ_i]			+10% -10%
✖Refractive Index of Medium 2 refers to the measure of how much a light ray is bent when it travels from medium 1 to medium 2, indicating the optical density of medium 2.ⓘ Refractive Index of Medium 2 [n₂]			+10% -10%

✖Refracted angle refers to the change in direction or bending of a light ray as it passes from one medium to another, due to the difference in the optical properties of the two media.ⓘ Refracted Angle using Snell's Law [θ_r]

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Formula

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Refracted Angle using Snell's Law

Formula

`"θ"_{"r"} = arcsinh(("n"_{"1"}*sin("θ"_{"i"}))/("n"_{"2"}))`

Example

`"18.46714°"=arcsinh(("1.01"*sin("30°"))/("1.54"))`

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Refracted Angle using Snell's Law Solution

STEP 0: Pre-Calculation Summary

Formula Used

Refracted Angle = arcsinh((Refractive Index of Medium 1*sin(Incident Angle))/(Refractive Index of Medium 2))
θ_r = arcsinh((n₁*sin(θ_i))/(n₂))
This formula uses 3 Functions, 4 Variables

Functions Used

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., sin(Angle)
sinh - The hyperbolic sine function, also known as the sinh function, is a mathematical function that is defined as the hyperbolic analogue of the sine function., sinh(Number)
arcsinh - The inverse hyperbolic sine function, also known as the arcsinh function, is the inverse function of the hyperbolic sine function., arcsinh(Number)

Variables Used

Refracted Angle - (Measured in Radian) - Refracted angle refers to the change in direction or bending of a light ray as it passes from one medium to another, due to the difference in the optical properties of the two media.
Refractive Index of Medium 1 - Refractive Index of Medium 1 represents the ratio of the speed of light in a vacuum to the speed of light in medium 1. It quantifies the optical density of the medium.
Incident Angle - (Measured in Radian) - The incident angle refers to the angle between the impact direction and the solid surface. For a vertical impact, this angle is 90 degrees.
Refractive Index of Medium 2 - Refractive Index of Medium 2 refers to the measure of how much a light ray is bent when it travels from medium 1 to medium 2, indicating the optical density of medium 2.

STEP 1: Convert Input(s) to Base Unit

Refractive Index of Medium 1: 1.01 --> No Conversion Required
Incident Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Refractive Index of Medium 2: 1.54 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_r = arcsinh((n₁*sin(θ_i))/(n₂)) --> arcsinh((1.01*sin(0.5235987755982))/(1.54))

Evaluating ... ...

θ_r = 0.322312431602421

STEP 3: Convert Result to Output's Unit

0.322312431602421 Radian -->18.4671420154212 Degree (Check conversion here)

FINAL ANSWER

18.4671420154212 ≈ 18.46714 Degree <-- Refracted Angle

(Calculation completed in 00.020 seconds)

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< 7 Laws of Illumination Calculators

Beer-Lambert Law

Go Intensity of Transmitted Light = Intensity of Light Entering the Material*exp(-Absorption per Concentration Coefficient*Concentration of Absorption Material*Path Length)

Fresnel's Law of Reflection

Go Reflection Loss = (Refractive Index of Medium 2-Refractive Index of Medium 1)^2/(Refractive Index of Medium 2+Refractive Index of Medium 1)^2

Refracted Angle using Snell's Law

Go Refracted Angle = arcsinh((Refractive Index of Medium 1*sin(Incident Angle))/(Refractive Index of Medium 2))

Incident Angle using Snell's Law

Go Incident Angle = arcsinh((Refractive Index of Medium 2*sin(Refracted Angle))/(Refractive Index of Medium 1))

Illumination by Lambert Cosine Law

Go Illumination Intensity = (Luminous Intensity*cos(Illumination Angle))/(Length of Illumination^2)

Lambert's Cosine Law

Go Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle)

Inverse Square Law

Go Luminance = Intensity of Transmitted Light/Distance^2

< 16 Advanced Illumination Calculators

Beer-Lambert Law

Go Intensity of Transmitted Light = Intensity of Light Entering the Material*exp(-Absorption per Concentration Coefficient*Concentration of Absorption Material*Path Length)

Fresnel's Law of Reflection

Go Reflection Loss = (Refractive Index of Medium 2-Refractive Index of Medium 1)^2/(Refractive Index of Medium 2+Refractive Index of Medium 1)^2

Refracted Angle using Snell's Law

Go Refracted Angle = arcsinh((Refractive Index of Medium 1*sin(Incident Angle))/(Refractive Index of Medium 2))

Incident Angle using Snell's Law

Go Incident Angle = arcsinh((Refractive Index of Medium 2*sin(Refracted Angle))/(Refractive Index of Medium 1))

Intensity of Light Transmitted

Go Intensity of Transmitted Light = Intensity of Light Entering the Material*exp(-Absorption Coefficient*Path Length)

Illumination by Lambert Cosine Law

Go Illumination Intensity = (Luminous Intensity*cos(Illumination Angle))/(Length of Illumination^2)

Number of Floodlighting Units

Go Number of Floodlighting Units = (Area to be Lighted*Illumination Intensity)/(0.7*Lumen Flux)

Lambert's Cosine Law

Go Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle)

Spectral Transmission Factor

Go Spectral Transmission Factor = Transmitted Spectral Emission/Spectral Irradiation

Spectral Reflection Factor

Go Spectral Reflection Factor = Reflected Spectral Emission/Spectral Irradiation

Utilization Factor of Electrical Energy

Go Utilization Factor = Lumen Reaching Working Plane/Lumen Emitting from Source

Spectral Luminous Efficacy

Go Spectral Luminous Efficacy = Maximum Sensitivity*Photopic Efficiency Value

Inverse Square Law

Go Luminance = Intensity of Transmitted Light/Distance^2

Specific Consumption

Go Specific Consumption = (2*Input Power)/Candle Power

Luminance for Lambertian Surfaces

Go Luminance = Illumination Intensity/pi

Luminous Intensity

Go Luminous Intensity = Lumen/Solid Angle

Refracted Angle using Snell's Law Formula

Refracted Angle = arcsinh((Refractive Index of Medium 1*sin(Incident Angle))/(Refractive Index of Medium 2))
θ_r = arcsinh((n₁*sin(θ_i))/(n₂))

How does Snell's law apply to refraction?

Snell's Law states that when visible light enters a transparent material at an angle, the direction of the light is refracted or bent at a different angle. Snell's Law is an equation that determines the angle at which a ray or beam of light is refracted.

How to Calculate Refracted Angle using Snell's Law?

Refracted Angle using Snell's Law calculator uses Refracted Angle = arcsinh((Refractive Index of Medium 1*sin(Incident Angle))/(Refractive Index of Medium 2)) to calculate the Refracted Angle, The Refracted Angle using Snell's Law formula is defined as “The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given colour and for the given pair of media”. Refracted Angle is denoted by θ_r symbol.

How to calculate Refracted Angle using Snell's Law using this online calculator? To use this online calculator for Refracted Angle using Snell's Law, enter Refractive Index of Medium 1 (n₁), Incident Angle (θ_i) & Refractive Index of Medium 2 (n₂) and hit the calculate button. Here is how the Refracted Angle using Snell's Law calculation can be explained with given input values -> 1178.473 = arcsinh((1.01*sin(0.5235987755982))/(1.54)).

FAQ

What is Refracted Angle using Snell's Law?

The Refracted Angle using Snell's Law formula is defined as “The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given colour and for the given pair of media” and is represented as θ_r = arcsinh((n₁*sin(θ_i))/(n₂)) or Refracted Angle = arcsinh((Refractive Index of Medium 1*sin(Incident Angle))/(Refractive Index of Medium 2)). Refractive Index of Medium 1 represents the ratio of the speed of light in a vacuum to the speed of light in medium 1. It quantifies the optical density of the medium, The incident angle refers to the angle between the impact direction and the solid surface. For a vertical impact, this angle is 90 degrees & Refractive Index of Medium 2 refers to the measure of how much a light ray is bent when it travels from medium 1 to medium 2, indicating the optical density of medium 2.

How to calculate Refracted Angle using Snell's Law?

The Refracted Angle using Snell's Law formula is defined as “The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given colour and for the given pair of media” is calculated using Refracted Angle = arcsinh((Refractive Index of Medium 1*sin(Incident Angle))/(Refractive Index of Medium 2)). To calculate Refracted Angle using Snell's Law, you need Refractive Index of Medium 1 (n₁), Incident Angle (θ_i) & Refractive Index of Medium 2 (n₂). With our tool, you need to enter the respective value for Refractive Index of Medium 1, Incident Angle & Refractive Index of Medium 2 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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