Mathematics of Two Point source interference

MATHEMATICS OF TWO POINT SOURCE INTERFERENCE

Anatomy of a two point source interference pattern

• central antinodal line: antinodal line
• first antinodal line (1) / second antinodal line (2): etc. antinodal lines are present to the left and right of central antinodal line
• order number (m): each line in the pattern is assigned a number

The Path Difference

• from point A on the first antinodal line (m = 1) the path difference is equivalent to 1 wavelength
• two point source interference pattern with values:

Explaining the Path difference equation

• diagram shows two waves traveling along different paths from different sources to the same point in such a way that a crest is meeting a crest
• constructive interference will occur at this point
• the waves from source 1 (S1) travels a distance of 6 wavelengths 
• the wave from source 2 (S2) travels a distance of & wavelengths to reach the same point
• the difference in distance traveled by the two waves is one full wavelength
• when the path difference is one full wavelength, a crest meets a crest and constructive interference occurs

Young’s Equation

• circular waves from two sources can interfere in the surrounding space to produce a pattern of antinodes and nodes
• the nodal positions are present at locations where destructive interference always occurs and the path difference is a half-number of wavelengths
• the antinodal potions are present at locations where constructive interference always occurs and the path difference is equivalent to a whole number of wavelengths
• 

A light interference pattern

• two point source interference pattern, light waves from two coherent, monochromatic sources will interfere constructively and destructively to produce a pattern of antinodes and nodes
• light traveling in air is usually not seen because there is nothing of substantial size in the air to reflect the light to our eyes. Therefore the pattern formed by light interference can’t be seen it is somehow projected onto some form of a screen or a sheet of paper
• locations where light constructively interferes corresponds to an abnormally bright spot
• locations where light destructively interferes corresponds to an abnormally dark spot
• maxima: antinodes are locations where light from the two individual sources are reinforcing each other and correspond to points of brightness or maximum intensity
• minima: nodes are location where light from the two individual sources are destroying each other and correspond to points of darkness or minimum intensity 

Young’s experiment

= y • d / (m • L)

• in 1801, Young devised and performed an experiment to measure the wavelength of light