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Path Difference in Young's Double-Slit Experiment Formula

GoPath Difference in YDSE given Distance between Coherent Sources Formula

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Path Difference is the difference in distance traveled by two waves, which determines the phase shift between them, affecting the resulting interference pattern. Check FAQs

Δx = \sqrt{{(y + \frac{d}{2})}^{2} + D^{2}} - \sqrt{{(y - \frac{d}{2})}^{2} + D^{2}}

Δx - Path Difference?y - Distance from Center to Light Source?d - Distance between Two Coherent Sources?D - Distance between Slits and Screen?

Path Difference in Young's Double-Slit Experiment Example

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Here is how the Path Difference in Young's Double-Slit Experiment equation looks like with Values.

Here is how the Path Difference in Young's Double-Slit Experiment equation looks like with Units.

Here is how the Path Difference in Young's Double-Slit Experiment equation looks like.

2.8664 = \sqrt{{(5.852 + \frac{10.6}{2})}^{2} + {20.2}^{2}} - \sqrt{{(5.852 - \frac{10.6}{2})}^{2} + {20.2}^{2}}

2.8664cm = \sqrt{{(5.852cm + \frac{10.6cm}{2})}^{2} + {20.2cm}^{2}} - \sqrt{{(5.852cm - \frac{10.6cm}{2})}^{2} + {20.2cm}^{2}}

2.8664 = \sqrt{{(5.852 + \frac{10.6}{2})}^{2} + {20.2}^{2}} - \sqrt{{(5.852 - \frac{10.6}{2})}^{2} + {20.2}^{2}}

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Path Difference in Young's Double-Slit Experiment Solution

Follow our step by step solution on how to calculate Path Difference in Young's Double-Slit Experiment?

FIRST Step Consider the formula

Δx = \sqrt{{(y + \frac{d}{2})}^{2} + D^{2}} - \sqrt{{(y - \frac{d}{2})}^{2} + D^{2}}

Next Step Substitute values of Variables

∴

Δx = \sqrt{{(5.852cm + \frac{10.6cm}{2})}^{2} + {20.2cm}^{2}} - \sqrt{{(5.852cm - \frac{10.6cm}{2})}^{2} + {20.2cm}^{2}}

Next Step Convert Units

∴

Δx = \sqrt{{(0.0585m + \frac{0.106m}{2})}^{2} + {0.202m}^{2}} - \sqrt{{(0.0585m - \frac{0.106m}{2})}^{2} + {0.202m}^{2}}

Next Step Prepare to Evaluate

∴

Δx = \sqrt{{(0.0585 + \frac{0.106}{2})}^{2} + {0.202}^{2}} - \sqrt{{(0.0585 - \frac{0.106}{2})}^{2} + {0.202}^{2}}

Next Step Evaluate

∴

Δx = 0.0286640782938647m

Next Step Convert to Output's Unit

∴

Δx = 2.86640782938647cm

LAST Step Rounding Answer

∴

Δx = 2.8664cm

Path Difference in Young's Double-Slit Experiment Formula Elements

Variables

Functions

Path Difference

Path Difference is the difference in distance traveled by two waves, which determines the phase shift between them, affecting the resulting interference pattern.

Symbol: Δx

Measurement: LengthUnit: cm

Note: Value can be positive or negative.

Formulas to find Path Difference

Distance from Center to Light Source

Distance from Center to Light Source is the length of the line segment from the center of the light source to the point of interest, used to calculate the intensity of light at that point.

Symbol: y

Measurement: LengthUnit: cm

Note: Value can be positive or negative.

Formulas to find Distance from Center to Light Source

Distance between Two Coherent Sources

Distance between Two Coherent Sources is the distance between two sources that emit waves in phase with each other, resulting in an interference pattern.

Symbol: d

Measurement: LengthUnit: cm

Note: Value can be positive or negative.

Formulas to find Distance between Two Coherent Sources

Distance between Slits and Screen

Distance between Slits and Screen is the distance between the slits and the screen in a Young's double-slit experiment, used to measure the interference pattern of light waves.

Symbol: D

Measurement: LengthUnit: cm

Note: Value should be greater than 0.

Formulas to find Distance between Slits and Screen

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.

Syntax: sqrt(Number)

Other Formulas to find Path Difference

Go Path Difference in YDSE given Distance between Coherent Sources

Δx = d \cdot \sin (θ)

Other formulas in Young's Double Slit Experiment (YDSE) category

Go Path Difference for Constructive Interference in YDSE

Δx CI = \frac{y CI \cdot d}{D}

Go Path Difference for Maxima in YDSE

Δx max = n \cdot λ

Go Path Difference for Minima in YDSE

Δx min = (2 \cdot n + 1) \cdot \frac{λ}{2}

Go Path Difference for Destructive Interference in YDSE

Δx DI = (2 \cdot n - 1) \cdot (\frac{λ}{2})

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

Path Difference in Young's Double-Slit Experiment evaluator 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 evaluate the Path Difference, Path Difference in Young's Double-Slit Experiment formula is defined as the difference in path lengths of the light waves that travel from the two slits to a point on the screen, which determines the interference pattern observed in the experiment. It is a crucial concept in understanding the principles of wave optics and interference. Path Difference is denoted by Δx symbol.

How to evaluate Path Difference in Young's Double-Slit Experiment using this online evaluator? To use this online evaluator 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.

FAQs on Path Difference in Young's Double-Slit Experiment

What is the formula to find Path Difference in Young's Double-Slit Experiment?

The formula of Path Difference in Young's Double-Slit Experiment is expressed as 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). Here is an example- 286.6408 = sqrt((0.05852+0.106/2)^2+0.202^2)-sqrt((0.05852-0.106/2)^2+0.202^2).

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

With Distance from Center to Light Source (y), Distance between Two Coherent Sources (d) & Distance between Slits and Screen (D) we can find Path Difference in Young's Double-Slit Experiment using the formula - 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). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Path Difference?

Here are the different ways to Calculate Path Difference-

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

Can the Path Difference in Young's Double-Slit Experiment be negative?

Yes, the Path Difference in Young's Double-Slit Experiment, measured in Length can be negative.

Which unit is used to measure Path Difference in Young's Double-Slit Experiment?

Path Difference in Young's Double-Slit Experiment is usually measured using the Centimeter[cm] for Length. Meter[cm], Millimeter[cm], Kilometer[cm] are the few other units in which Path Difference in Young's Double-Slit Experiment can be measured.

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Path Difference in Young's Double-Slit Experiment Formula

​GoPath Difference in YDSE given Distance between Coherent Sources Formula

Path Difference in Young's Double-Slit Experiment Example

Path Difference in Young's Double-Slit Experiment Solution

Path Difference in Young's Double-Slit Experiment Formula Elements

Other Formulas to find Path Difference

Other formulas in Young's Double Slit Experiment (YDSE) category

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

FAQs on Path Difference in Young's Double-Slit Experiment

Variable Name

GoPath Difference in YDSE given Distance between Coherent Sources Formula