A parallel beam of white light falls on a thin film whose refractive index is equal to `4//3` . The angle of incidence `i=53^(@)` What must be the minimum film thickness, if the reflected light is to be coloured yellow `(lambda "of yellow" =0.6mum)` most intensity ? `(tan 53^(@)=4//3)`

Explanation

From the relation,
`mu=(sini)/(sin r)rArr 4/3=(sin 53^(@))/(sin r)`
We have `r approx 37^(@)`
Interference has to be taken between rays 1 and 2 They have already a phase difference of `pi` because ray 1 is reflected from a denser medium.

They have a path difference of
`Deltax=2mu(AD)-AB`
`=2mu(t/cosr)-2t(tanr)(sin i)`
`=2(4/3)(5/3)t-2(t)(3/4)(4/5)=32/15 t`
For the two waves to interfere constructively,
`Deltax=(2n-1)lambda/2 (where, n=1,2,3,...)`
`or 32/15 t=(2n-1)lambda/2`
For minima thickness, n=1
or `32/15t=lambda/2`
or `t=15/64 lambda`
`=(15xx0.6)/64 mum=0.14 mum`