Newton rings: spherical droplet with thin film interference

[insomnia]

Homework Statement

So I have a similar situation with the traditional Newton rings. Instead of having however a convex lens, I have a (partial) spherical surface with height d with sitting on top of a thin film of thickness t, with d >>> t, and refractive index n and below the thin film is a mirror. I have to find what is the condition for constructive/destructive interference for the resulting Newton rings.

Homework Equations

The Attempt at a Solution

I know that: i have optical length inside the spherical surface of the would be [tex]d[/tex], so the optical path would be [tex]2d[/tex]. Also, I have an optical length inside the thin film, where there would also be a phase change of [tex]\pi[/tex]. So total change of phase would be [tex]2d+2t+\pi[/tex].

Also, from the geometry You can infer that:[tex] r_m^2 = t*(2R-t)[/tex] where [tex]r_m[/tex] would be the radius of the mth dark ring and [tex]R[/tex] the radius the circle (curvature of the lense).

Any advice welcomed. Many thanks

 

[anathema]

!

Thank you for sharing your situation with the traditional Newton rings. It sounds like you have a challenging problem to solve. Based on the information you have provided, here are some suggestions for finding the condition for constructive/destructive interference for the resulting Newton rings:

1. Start by reviewing the general equation for constructive and destructive interference: 2nt = (m + 1/2)λ for constructive interference and 2nt = mλ for destructive interference, where n is the refractive index, t is the thickness of the thin film, m is the order of the interference, and λ is the wavelength of light.

2. Consider the geometry of your setup and how it may affect the path length of the light traveling through the spherical surface and the thin film. Remember that for constructive interference, the path length difference must be equal to an integer multiple of the wavelength, while for destructive interference, it must be equal to a half-integer multiple.

3. Use the information you have about the optical length inside the spherical surface and the thin film to calculate the total path length difference and determine the conditions for constructive and destructive interference.

4. Take into account the phase change of π that occurs when light reflects off a mirror. This will affect the total phase difference and may change the conditions for constructive and destructive interference.

5. Finally, use the equation you mentioned relating the radius of the mth dark ring to the thickness of the thin film and the curvature of the lens to verify your results.

I hope these suggestions are helpful in finding a solution to your problem. Good luck with your research!