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We for equal wave intensities the intensity at a point is given by  but where does the formula  come from??
Asked by deepsmooth41 | 19 Apr, 2020, 01:00: AM
When two waves of exactly same frequency travels in a medium,  in the same direction simultaneoulsy then due to their superposition, inetnsity of light is maximum at some point and minimum at some points.
When the intensity at certain point is maximum,
I = Imax cos2 (Φ/2)
For consructive interference,
When two waves meet a point at same phase, constructive interference occurs (i.e maximum light)
Here, phase difference,  Φ = 0º or 2n∏
Path difference, Δ = nλ
resultant amplitude,
Amax = a1 + a2 = 2a0 (since, a0 = a1 =  a2 )

Resultant intensity is,
Imax = I1 + I2 +2 √(I1 I2 ) = (√I1 + √I2)2
If,
I0  = I1 = I2

Imax = 4I0

Hence,

I =4I0 cos2 (Φ/2)
**********************************************************************************************************
OR

If two waves having same frequency but have certain fixed phase difference 'Φ' between them, then the resultant intensity,
I  = I1 + I2 +2 √(I1 I2 ) cosΦ
For two identical source,
I0  = I1 = I2
Hence,

I = I0 +I0 +2 √(I0 I0  ) cosΦ
I = 4I0 cos2 (Φ/2) .... (as, 1 + cosθ = 2cos2 (θ/2) )

Answered by Shiwani Sawant | 19 Apr, 2020, 05:08: PM

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