Optics – Newton Rings

1. The problem statement, all variables and given/known data

These are problems from a Newton rings experiment where a lens was placed on a flat surface and the interference patterns created Newton rings. I measured the diameter of the first five rings and then plotted a graph of d^2 against N (number of the individual ring).

These are my x and y values:

N D^2
1 0.011 mm
2 0.019 mm
3 0.029 mm
4 0.038 mm
5 0.048 mm

From this, I found the slope of the graph and the intercept of the line on the y axis as I got an equation of y=0.0093x+ 0.0011. From this, I was told to graphically calculate r (radius of curvature of unknown lens) and then calculate r for each ring using the formula d^2 = 4 (lamba) r N + constant where lamba = 589.3 nm and the constant is the y-intercept.

This is what the first question is asking…
1. What is the radius of curvature of this lens? Show your results as separate calculations for each value of N.

After doing this, I am required to calculate the power of the lens, assuming the refractive index of the lens is 1.523.
2. Relevant equations

y=0.0093x+0.0011 which translates to…
d^2 = [4*lamba*r]N + b

F = n’-n/r (for power of the lens after finding r)
3. The attempt at a solution

For the first part where it says graphically calculate r from the slope:

y=0.0093x + 0.0011

I am unsure how to get radius from this…

I tried:
9300 nm^2 = 4 (589.3 nm)(r)
r = 3.95 mm but this seems incorrect…

I would really appreciate help on this!

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