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A Thin film of oil ( n=1.25) is located on a smooth wet pavement. When viewed perpendicular to the pavement, the film reflects most strongly red light at 640nm and reflect no blue light at 512nm. How thick is the oil film?

[tex]\lambda_C=640nm[/tex] Constructive interference

[tex]\lambda_D=512nm[/tex] Destructive interference

We know that the light has to travel to three different mediums,

air,oil,and water.

So..

[tex]n_1=1.00[/tex] which is air.

[tex]n_2=1.25[/tex] which is oil.

[tex]n_3=1.33[/tex] which is water.

Since we know the second medium has a higher index of refraction then water.

[tex] n_2 > n_1[/tex]

so our change in phase is [tex]\DELTA a = \lambda/2 [/tex]

Our second refraction is caused by the light hitting the oil and reaching the surface of water and going back up.

So

[tex]

n_2 < n_3

[\tex]

so our change there is

[tex]

\DELTA b = 2t+ \lamda/2

[/tex]

Therefore, the relative shift is

[tex]

\delta=\delta b - \delta a=2t+\lamda/2-lambda/2=2t

[/tex]

So we se tthat equal to constructive interference

and we get

[tex]2t=m\lamda_c[/tex]

[tex]t=m\lambda_c/2[/tex]

so t=320nm.

So in the similar fashion, i can find the thickness t for destructive interference.

instead of setting [tex] 2t=m\lambda_c, I can set 2t=(m+1/2)\lamda_c)[/tex]

and by setting m = 1

I find t= 128nm..

so my question is? I have two different thicknesses, how do i 'combine them' or manipulate them to get my total thickness?