White light may be considered to be mixture of waves of `lambda` ranging between `3900 Å` and `7800 Å`. An oil film of thickness `10,000 Å` is examined normally by the reflected light. If `mu=1.4`, then the film appears bright for

Explanation

The condition for dark fringe or weak reflection when seen in reflected light is `2mu t cos r = n lambda`, where n is an integer.
For normal incidence, r = 0 and cos r = 1
so that `2 mu t = n lambda`
or `lambda = (2mu t)/(n)`
Substituting the values of `mu` and t, we get
`lambda = (2xx1.4xx10^(-6))/(n)=(28xx10^(-7))/(n)m`
For values of n `lt 4` or `gt 7`, the values of `lambda` do not lie in the visible range 4000 Å to 7500 Å. But for values of n = 4, 5, 6, 7, the following wavelengths lie in the visible region :
(i) `lambda = (28xx10^(-7))/(4)`
`=7.0xx10^(-7)m`
`=7000 Å`
(ii) `lambda =(28xx10^(-7))/(5)`
`= 5.6xx10^(-7)m`
`= 5600 Å`
(iii) `lambda = (28x10^(-7))/(6)`
`= 4.667xx10^(-7)m`
`= 4667 Å`
(iv) `lambda = (28xx10^(-7))/(7)`
`=4.0xx10^(-7)m`
`= 4000 Å`
The condition for bright fringe or strong reflection is
`2mu t=((2n + 1)lambda)/(2)`
or `lambda =(4mu t)/((2n+1))`
Substituting the values of `mu` and t, we get
`lambda = (4xx1.4xx10^(-6))/(2n+1)`
`=(56+10^(-7))/(2n+1)m`
For values of n `lt 4` or `gt 6`, the values of `lambda` do not lie in the visible range. But for n = 4, 5, 6 the following waelengths lie in the visible range :
(i) `lambda = (56xx10^(-7))/(2xx4+1)`
`=6.222xx10^(-7)m`
`=6222 Å`