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

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To determine the refractive index of the liquid in a Newton's rings experiment, the diameter of the rings before and after introducing the liquid is crucial. The original diameter of the fourth bright ring is 10.0 mm, which decreases to 8.45 mm when the liquid is added. The relevant equation for calculating the radius of the Nth ring is xm=√mλfR. The refractive index can be calculated based on the change in diameter, considering the properties of the liquid and the glass used in the experiment. Understanding these principles is essential for solving the problem effectively.
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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.
 
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ChrisWM said:
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 Nth ring?
https://en.m.wikipedia.org/wiki/Newton's_rings#Theory
 

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