Question

Derive the conditions of maxima and minima due to interference of light transmitted from thin film of uniform thickness.

Answer 1

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)`
`= 2μtcosr(1−sin^2r)`
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`