## Path difference in Young's double-slit experiment Solution

STEP 0: Pre-Calculation Summary
Formula Used
Path Difference = sqrt((Distance from center to the light source+(Distance between two coherent sources/2))^2+(Distance between slits and screen)^2)-sqrt((Distance from center to the light source-(Distance between two coherent sources/2))^2+(Distance between slits and screen)^2)
k = sqrt((y+(d/2))^2+(D)^2)-sqrt((y-(d/2))^2+(D)^2)
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - Squre root function, 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 the light source - (Measured in Meter) - Distance from center to the 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 the light source: 2 Centimeter --> 0.02 Meter (Check conversion here)
Distance between two coherent sources: 10 Centimeter --> 0.1 Meter (Check conversion here)
Distance between slits and screen: 20 Centimeter --> 0.2 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
k = sqrt((y+(d/2))^2+(D)^2)-sqrt((y-(d/2))^2+(D)^2) --> sqrt((0.02+(0.1/2))^2+(0.2)^2)-sqrt((0.02-(0.1/2))^2+(0.2)^2)
Evaluating ... ...
k = 0.00965871684260405
STEP 3: Convert Result to Output's Unit
0.00965871684260405 Meter --> No Conversion Required
0.00965871684260405 Meter <-- Path Difference
(Calculation completed in 00.031 seconds)
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Created by Payal Priya
Birsa Institute of Technology (BIT), Sindri
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## < 10+ Young's double-slit experiment Calculators

Path difference in Young's double-slit experiment
Path Difference = sqrt((Distance from center to the light source+(Distance between two coherent sources/2))^2+(Distance between slits and screen)^2)-sqrt((Distance from center to the light source-(Distance between two coherent sources/2))^2+(Distance between slits and screen)^2) Go
Resultant intensity on-screen of YDSE when intensities are different
Resultant Intensity = Intensity 1+Intensity 2+(2*sqrt(Intensity 1*Intensity 2)*cos(Phase Difference)) Go
Distance from center to light source for destructive interference in YDSE in terms of wavelength
Distance from center to the light source = ((2*Number-1)*Wavelength*Distance between slits and screen)/(2*Distance between two coherent sources) Go
Distance from center to light source for constructive interference in YDSE
Distance from center to the light source = (Number*Wavelength*Distance between slits and screen)/Distance between two coherent sources Go
Path difference for constructive interference in Young's double-slit experiment
Path Difference = (Distance between two coherent sources*Distance from center to the light source)/Distance between slits and screen Go
Path difference in YDSE in terms of Distance between Coherent Sources
Path Difference = Distance between two coherent sources*sin(Theta) Go
Resultant intensity on-screen of Young's double-slit experiment
Resultant Intensity = 4*Intensity 1*(cos(Phase Difference/2))^2 Go
Distance from center to light source for destructive interference in YDSE
Distance from center to the light source = (((2*Number)+1)*Wavelength)/2 Go
Resultant intensity of coherent sources
Resultant Intensity = Intensity 1+Intensity 2 Go
Path difference for minima in YDSE
Path Difference = (2*Number+1)*Wavelength/2 Go

## Path difference in Young's double-slit experiment Formula

Path Difference = sqrt((Distance from center to the light source+(Distance between two coherent sources/2))^2+(Distance between slits and screen)^2)-sqrt((Distance from center to the light source-(Distance between two coherent sources/2))^2+(Distance between slits and screen)^2)
k = sqrt((y+(d/2))^2+(D)^2)-sqrt((y-(d/2))^2+(D)^2)

## 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 the light source+(Distance between two coherent sources/2))^2+(Distance between slits and screen)^2)-sqrt((Distance from center to the 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 k 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 the 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 -> 0.009659 = sqrt((0.02+(0.1/2))^2+(0.2)^2)-sqrt((0.02-(0.1/2))^2+(0.2)^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 k = sqrt((y+(d/2))^2+(D)^2)-sqrt((y-(d/2))^2+(D)^2) or Path Difference = sqrt((Distance from center to the light source+(Distance between two coherent sources/2))^2+(Distance between slits and screen)^2)-sqrt((Distance from center to the light source-(Distance between two coherent sources/2))^2+(Distance between slits and screen)^2). Distance from center to the 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 the light source+(Distance between two coherent sources/2))^2+(Distance between slits and screen)^2)-sqrt((Distance from center to the 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 the 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 the 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 the light source, Distance between two coherent sources & Distance between slits and screen. We can use 5 other way(s) to calculate the same, which is/are as follows -
• Path Difference = Distance between two coherent sources*sin(Theta)
• Path Difference = (2*Number+1)*Wavelength/2
• Path Difference = (Distance between two coherent sources*Distance from center to the light source)/Distance between slits and screen
• Path Difference = (2*Number-1)*Wavelength/2
• Path Difference = Number*Wavelength
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