We for equal wave intensities the intensity at a point is given by straight I to the power of apostrophe equals 4 Icos squared open parentheses straight ϕ over 2 close parentheses but where does the formula straight I to the power of apostrophe equals Icos squared open parentheses straight ϕ over 2 close parentheses come from??

Asked by deepsmooth41 | 19th Apr, 2020, 01:00: AM

Expert Answer:

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)
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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 | 19th Apr, 2020, 05:08: PM