How Does Water Alter the Diameter of Newton's Rings?

[Frosty128]

Homework Statement

Newton's rings can be seen when a planoconvex lens is placed on a flat glass surface. For a particular lens with an index of refraction of n= 1.51 and a glass plate with an index of n= 1.78, the diameter of the third bright ring is 0.760 mm.

If water (n= 1.33) now fills the space between the lens and the plate, what is the new diameter of this ring?

Homework Equations

r_N = [(N-0.5)λR]^1/2

r=radius of N^th bright ring
N=ring number
λ=wavelength of light that passes through the glass
R=radius of curvature of the lens

The Attempt at a Solution

If I was given a value for λ for the wavelength of light, I know I could simply plug in everything to find the radius of curvature of the planoconvex lens, then divide λ by 1.33 and solve for the new r₃, but with the given data I am not sure how to find the wavelength of light, or if there is some other way to go about solving this problem.

 

[Frosty128]

I forgot to mention that, since this is the third bright ring, this must be the third instance of constructive interference, so that the thickness of the film at that point must equal (3/2)λ, but I do not know where to go from there.