Path Difference in Young's Double-Slit Experiment Calculator

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Young's Double-Slit Experiment (YDSE)

Basics

Interference of Waves of Two Intensities

Optical Path Difference

Thin-Film Interference

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Path Difference in YDSE

✖Distance from Center to Light Source is the length from the center of the slit to the light source.ⓘ Distance from Center to Light Source [y]			+10% -10%
✖Distance between Two Coherent Sources is the length at which both coherent sources are placed. Two sources that vibrate with a fixed phase difference between them are said to be coherent.ⓘ Distance between Two Coherent Sources [d]			+10% -10%
✖Distance between Slits and Screen or photodetector is the large distance at which the slits and screen in Young's double-slit experiment.ⓘ Distance between Slits and Screen [D]			+10% -10%

✖The Path Difference or PD is the difference in distance traveled by the two waves from their respective sources to a given point on the pattern.ⓘ Path Difference in Young's Double-Slit Experiment [Δx]

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Formula

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Path Difference in Young's Double-Slit Experiment

Formula

`"Δx" = sqrt(("y"+"d"/2)^2+"D"^2)-sqrt(("y"-"d"/2)^2+"D"^2)`

Example

`"1.260501cm"=sqrt(("2.5cm"+"10.6cm"/2)^2+("20.2cm")^2)-sqrt(("2.5cm"-"10.6cm"/2)^2+("20.2cm")^2)`

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Path Difference in Young's Double-Slit Experiment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Path Difference = sqrt((Distance from Center to Light Source+Distance between Two Coherent Sources/2)^2+Distance between Slits and Screen^2)-sqrt((Distance from Center to Light Source-Distance between Two Coherent Sources/2)^2+Distance between Slits and Screen^2)
Δx = sqrt((y+d/2)^2+D^2)-sqrt((y-d/2)^2+D^2)
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Path Difference - (Measured in Meter) - The Path Difference or PD is the difference in distance traveled by the two waves from their respective sources to a given point on the pattern.
Distance from Center to Light Source - (Measured in Meter) - Distance from Center to Light Source is the length from the center of the slit to the light source.
Distance between Two Coherent Sources - (Measured in Meter) - Distance between Two Coherent Sources is the length at which both coherent sources are placed. Two sources that vibrate with a fixed phase difference between them are said to be coherent.
Distance between Slits and Screen - (Measured in Meter) - Distance between Slits and Screen or photodetector is the large distance at which the slits and screen in Young's double-slit experiment.

STEP 1: Convert Input(s) to Base Unit

Distance from Center to Light Source: 2.5 Centimeter --> 0.025 Meter (Check conversion here)
Distance between Two Coherent Sources: 10.6 Centimeter --> 0.106 Meter (Check conversion here)
Distance between Slits and Screen: 20.2 Centimeter --> 0.202 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Δx = sqrt((y+d/2)^2+D^2)-sqrt((y-d/2)^2+D^2) --> sqrt((0.025+0.106/2)^2+0.202^2)-sqrt((0.025-0.106/2)^2+0.202^2)

Evaluating ... ...

Δx = 0.0126050100771699

STEP 3: Convert Result to Output's Unit

0.0126050100771699 Meter -->1.26050100771699 Centimeter (Check conversion here)

FINAL ANSWER

1.26050100771699 ≈ 1.260501 Centimeter <-- Path Difference

(Calculation completed in 00.004 seconds)

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< 6 Path Difference in YDSE Calculators

Path Difference in Young's Double-Slit Experiment

Go Path Difference = sqrt((Distance from Center to Light Source+Distance between Two Coherent Sources/2)^2+Distance between Slits and Screen^2)-sqrt((Distance from Center to Light Source-Distance between Two Coherent Sources/2)^2+Distance between Slits and Screen^2)

Path Difference for Constructive Interference in YDSE

Go Path Difference = (Distance from Center to Light Source*Distance between Two Coherent Sources)/Distance between Slits and Screen

Path Difference in YDSE given Distance between Coherent Sources

Go Path Difference = Distance between Two Coherent Sources*sin(Angle from Slit Center to Light Source)

Path Difference for Destructive Interference in YDSE

Go Distance from Center to Light Source = (2*Number n+1)*Wavelength/2

Path Difference for Minima in YDSE

Go Path Difference = (2*Number n+1)*Wavelength/2

Path Difference for Maxima in YDSE

Go Path Difference = Number n*Wavelength

Path Difference in Young's Double-Slit Experiment Formula

What is Young's double-slit experiment ?

Young’s double-slit experiment uses two coherent sources of light placed at a small distance apart, usually, only a few orders of magnitude greater than the wavelength of light is used. Young’s double-slit experiment helped in understanding the wave theory of light. A screen or photodetector is placed at a large distance ’D’ away from the slits.

Why path difference is created between two coherent sources? How path difference is calculated?

The wave reaching light source from the second coherent source must travel a longer path than the wave reaching light source from the first coherent source. It is calculated by formula Δp = √( ( y+d/2)² + D²) - √( ( y-d/2)² + D²) where y is the distance from center of the screen to the light source , D is the distance between slits and screen or photodetector and d is the distance between two coherent sources.

How to Calculate Path Difference in Young's Double-Slit Experiment?

Path Difference in Young's Double-Slit Experiment calculator uses Path Difference = sqrt((Distance from Center to Light Source+Distance between Two Coherent Sources/2)^2+Distance between Slits and Screen^2)-sqrt((Distance from Center to Light Source-Distance between Two Coherent Sources/2)^2+Distance between Slits and Screen^2) to calculate the Path Difference, Path difference in Young's double-slit experiment is because the wave reaching light source from the second coherent source must travel a longer path than the wave reaching light source from the first coherent source. Path Difference is denoted by Δx symbol.

How to calculate Path Difference in Young's Double-Slit Experiment using this online calculator? To use this online calculator for Path Difference in Young's Double-Slit Experiment, enter Distance from Center to Light Source (y), Distance between Two Coherent Sources (d) & Distance between Slits and Screen (D) and hit the calculate button. Here is how the Path Difference in Young's Double-Slit Experiment calculation can be explained with given input values -> 126.0501 = sqrt((0.025+0.106/2)^2+0.202^2)-sqrt((0.025-0.106/2)^2+0.202^2).

FAQ

What is Path Difference in Young's Double-Slit Experiment?

Path difference in Young's double-slit experiment is because the wave reaching light source from the second coherent source must travel a longer path than the wave reaching light source from the first coherent source and is represented as Δx = sqrt((y+d/2)^2+D^2)-sqrt((y-d/2)^2+D^2) or Path Difference = sqrt((Distance from Center to Light Source+Distance between Two Coherent Sources/2)^2+Distance between Slits and Screen^2)-sqrt((Distance from Center to Light Source-Distance between Two Coherent Sources/2)^2+Distance between Slits and Screen^2). Distance from Center to Light Source is the length from the center of the slit to the light source, Distance between Two Coherent Sources is the length at which both coherent sources are placed. Two sources that vibrate with a fixed phase difference between them are said to be coherent & Distance between Slits and Screen or photodetector is the large distance at which the slits and screen in Young's double-slit experiment.

How to calculate Path Difference in Young's Double-Slit Experiment?

Path difference in Young's double-slit experiment is because the wave reaching light source from the second coherent source must travel a longer path than the wave reaching light source from the first coherent source is calculated using Path Difference = sqrt((Distance from Center to Light Source+Distance between Two Coherent Sources/2)^2+Distance between Slits and Screen^2)-sqrt((Distance from Center to Light Source-Distance between Two Coherent Sources/2)^2+Distance between Slits and Screen^2). To calculate Path Difference in Young's Double-Slit Experiment, you need Distance from Center to Light Source (y), Distance between Two Coherent Sources (d) & Distance between Slits and Screen (D). With our tool, you need to enter the respective value for Distance from Center to Light Source, Distance between Two Coherent Sources & Distance between Slits and Screen and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Path Difference?

In this formula, Path Difference uses Distance from Center to Light Source, Distance between Two Coherent Sources & Distance between Slits and Screen. We can use 4 other way(s) to calculate the same, which is/are as follows -

Path Difference = (Distance from Center to Light Source*Distance between Two Coherent Sources)/Distance between Slits and Screen
Path Difference = Number n*Wavelength
Path Difference = Distance between Two Coherent Sources*sin(Angle from Slit Center to Light Source)
Path Difference = (2*Number n+1)*Wavelength/2

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