Interference pattern for thin films

[devd]

Homework Statement

A parallel beam of light of wavelength $\lambda$ is incident normally on a thin polymer film with air on both sides. If the film has a refractive index $n>1$, then, for what value of the thickness, can second order bright fringes be observed in reflection?

Homework Equations

For normal incidence, condition for constructive interference is $$ 2nd=(m+1/2)\lambda$$ for integer m.

The Attempt at a Solution

Frankly, i don't understand the question. For parallel plane waves, the screen should have uniform illumination, light or dark according to whether $2nd=m\lambda$ or $2nd=(m+1/2)\lambda$, right?

What does one mean by 2nd order fringes in this context? Does it mean, we simply put $m=2$ and find the corresponding thickness?

 

[ecastro]

Yes, the equation you must use depends on whether you're computing for the bright or dark fringes.

You just need to substitute $m$ for the fringe order you need.

 

[devd]

Yes, the equation you must use depends on whether you're computing for the bright or dark fringes.

You just need to substitute $m$ for the fringe order you need.

My point is, there shouldn't be any fringe pattern on the screen at all! It should either be uniformly dark or uniformly bright according to which eqn the thickness satisfies. What, then, is meant by a fringe of 2nd order, in this context?

 

[ecastro]

It should either be uniformly dark or uniformly bright according to which eqn the thickness satisfies.

There is an interference pattern on the screen. That is why you see a "rainbow" of colors on soap bubbles.