Answer to Question #134984 in Electricity and Magnetism for Max

Question

A parallel beam of light of wavelength lembda is incident normally on a thin polymer film
with air on both sides. If the film has a refractive index n >1, then second-order bright
fringes can be observed in reflection when the thickness of the film is

Answer 1

As per the given question,

Wavelength light $=(\lambda)$

Refractive index of the film $=n$

$n>1$

Let the thickness of the film is $(t)$

As when the ray of light incident on the first film, then some part of the light reflect from the first surface and some part of light go to the second layer and then it get reflect from that surface.

total path difference between the first and second ray of light

$x= 2nt$

we know that $x=m\lambda$

But here it is second order bright fringes, so m=1 and for bright fringe it will be $(m+\frac{1}{2})$

So, $2nt = (2+\frac{1}{2})\lambda$

$\Rightarrow t=\dfrac{5\lambda}{4n}$