Derive the conditions of maxima and minima due to interference of light transmitted from thin film of uniform thickness.
Consider a thin film of uniform thickness (t) and R.I (μ)
On Reflected side,
The ray of light R1 and R2 will interfere.
The path difference between R1 and R2 is,
Δ = μ(BC + CD) − BG
`BC = CD = t/cosr `..........(1)
Now, BD = (2t) tan r .......(2)
BM = BD sin i
BM = (2t) tan r sin i
`BM = 2tμsinr(sinr / cosr)`
`BM = 2μt((sin^2r)/cosr) `..........(3)
Substituting (i) and (iii) in Δ :
`Δ = μ(t / cosr + t / cosr)−2μt((sin2r) / cosr)`
Δ = 2μtcosr
For transmitted system :
The transmitted rays CT1 and ET2 are also derived from the same incident ray AB and hence they are coherent.
Path difference = △ = μ(CD + DE) – CL
For constructive interference :
2μtcos r = n𝜆
For destructive interference :
`2μtcos r = (2n – 1)λ/2`