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Angle of Light Ray given Uncertainty in Position Calculator

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✖Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space or along a wire.ⓘ Wavelength [λ]			+10% -10%
✖Uncertainty in Position is the accuracy of the measurement of particle.ⓘ Uncertainty in Position [Δx]			+10% -10%

✖Theta given UP is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Angle of Light Ray given Uncertainty in Position [θ_UP]

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Angle of Light Ray given Uncertainty in Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theta given UP = asin(Wavelength/Uncertainty in Position)
θ_UP = asin(λ/Δx)
This formula uses 2 Functions, 3 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)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)

Variables Used

Theta given UP - (Measured in Radian) - Theta given UP is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
Wavelength - (Measured in Meter) - Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space or along a wire.
Uncertainty in Position - (Measured in Meter) - Uncertainty in Position is the accuracy of the measurement of particle.

STEP 1: Convert Input(s) to Base Unit

Wavelength: 2.1 Nanometer --> 2.1E-09 Meter (Check conversion here)
Uncertainty in Position: 35 Meter --> 35 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_UP = asin(λ/Δx) --> asin(2.1E-09/35)

Evaluating ... ...

θ_UP = 6E-11

STEP 3: Convert Result to Output's Unit

6E-11 Radian -->3.43774677078559E-09 Degree (Check conversion here)

FINAL ANSWER

3.43774677078559E-09 ≈ 3.4E-9 Degree <-- Theta given UP

(Calculation completed in 00.004 seconds)

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Angle of Light Ray given Uncertainty in Position Formula

LaTeX Go

Theta given UP = asin(Wavelength/Uncertainty in Position)
θ_UP = asin(λ/Δx)

What is Heisenberg's Uncertainty Principle?

Heisenberg's Uncertainty Principle states that ' It is impossible to determine simultaneously, the exact position as well as momentum of an electron'. It is mathematically possible to express the uncertainty that, Heisenberg concluded, always exists if one attempts to measure the momentum and position of particles. First, we must define the variable “x” as the position of the particle, and define “p” as the momentum of the particle.

Is Heisenberg’s Uncertainty Principle noticeable in All Matter Waves?

Heisenberg’s principle is applicable to all matter waves. The measurement error of any two conjugate properties, whose dimensions happen to be joule sec, like position-momentum, time-energy will be guided by the Heisenberg’s value.
But, it will be noticeable and of significance only for small particles like an electron with very low mass. A bigger particle with heavy mass will show the error to be very small and negligible.

How to Calculate Angle of Light Ray given Uncertainty in Position?

Angle of Light Ray given Uncertainty in Position calculator uses Theta given UP = asin(Wavelength/Uncertainty in Position) to calculate the Theta given UP, The Angle of light ray given uncertainty in position can be defined as the figure formed by two rays meeting at a common endpoint. Theta given UP is denoted by θ_UP symbol.

How to calculate Angle of Light Ray given Uncertainty in Position using this online calculator? To use this online calculator for Angle of Light Ray given Uncertainty in Position, enter Wavelength (λ) & Uncertainty in Position (Δx) and hit the calculate button. Here is how the Angle of Light Ray given Uncertainty in Position calculation can be explained with given input values -> 2E-7 = asin(2.1E-09/35).

FAQ

What is Angle of Light Ray given Uncertainty in Position?

The Angle of light ray given uncertainty in position can be defined as the figure formed by two rays meeting at a common endpoint and is represented as θ_UP = asin(λ/Δx) or Theta given UP = asin(Wavelength/Uncertainty in Position). Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space or along a wire & Uncertainty in Position is the accuracy of the measurement of particle.

How to calculate Angle of Light Ray given Uncertainty in Position?

The Angle of light ray given uncertainty in position can be defined as the figure formed by two rays meeting at a common endpoint is calculated using Theta given UP = asin(Wavelength/Uncertainty in Position). To calculate Angle of Light Ray given Uncertainty in Position, you need Wavelength (λ) & Uncertainty in Position (Δx). With our tool, you need to enter the respective value for Wavelength & Uncertainty in Position 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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