Young's double slit experiment

Principle of Superposition of wave

It states that if the no. Of waves travelling in the same direction in a medium then the total displacement of the resultant wave is given by vector sum of displacement of all individual waves 

Interference of wave                               

 when the 2 wave of same frequency and having zero or constant phase difference propagates in same direction superposed on each other then the intensity of resultant wave having minimum and maximum values at the particular point in the medium. This phenomenon is known as interference of wave. 

                                  Note

• the points at which the intensity of resultant wave is maximum is known as constructive interference. 

• the points at which the intensity of resultant wave is minimum is called destructive interference. 

Young's double slit experiment

Young's obtained interference pattern on the screen. 

                                    Note

• At where crest - crest or trough - trough suspended on each other we will get bright fringe at that in screen. 

• At where crest - trough superposed on each other we will get dark fringe at that place in screen. 

Condition for constructive and destructive interference

y1 = a1 sinwt

y2 = a2 sin(wt+phie) 

From Superposition

y = y1+y2

y = a1 sinwt + a2 sin(wt+phie) 

y = a1 sinwt + a2(sinwt cos(phie) + coswt sin(phie) ) 

y = a1 sinwt + a2 sinwt cos(phie) + a2 coswt sin(phie) 

y = (a1+a2 cos(phie) )sinwt + a2 sin(phie) coswt

On putting

a1+a2 cos(phie) = A cos(theta)  ..... (1) 

a2 sin(phie) = A sin(theta)         ......(2) 

y = A cos(theta) sinwt + A sin(theta) coswt

y = A sin(wt+phie) 

(1). Intensity will be maximum

When cos(phie) = 1

Cos(phie) = 0°, 2π, 4π, 6π

Phie = 0,2π, 4π, 6π

(2). Intensity will be minimum

       When cos(phie) = -1

        Cos(phie) = π, 3π, 5π

       And the path difference