How to Determine the Liquid's Refractive Index in a Newton's Rings Experiment?

[ChrisWM]

Homework Statement

Consider a Newton's ring experiment in air. The diameter of the fourth bright rings 10.0mm. When an unknown liquid is poured into the gap between the lens and the support, the diameter of this ring shrinks to 8.45 mm. Calculate the liquid's index of refraction. Assume that the liquid's refractive index is less than the index of refraction of glass (used for the lens and bottom plate).

Relevant Equations

xm=√mλfR.

I have no idea where to start with this. My professor didn't give an example and I am very confused.

 

[haruspex]

Homework Statement:: Consider a Newton's ring experiment in air. The diameter of the fourth bright rings 10.0mm. When an unknown liquid is poured into the gap between the lens and the support, the diameter of this ring shrinks to 8.45 mm. Calculate the liquid's index of refraction. Assume that the liquid's refractive index is less than the index of refraction of glass (used for the lens and bottom plate).
Relevant Equations:: xm=√mλfR.

I have no idea where to start with this. My professor didn't give an example and I am very confused.

What is the equation for the radius of the N^th ring?
https://en.m.wikipedia.org/wiki/Newton's_rings#Theory