Solving a Plano-Convex Lens Problem: The 100th Bright Ring

[AtticusFinch]

Homework Statement

A plano-convex lens having a radius of curvature of r = 4.00m is placed on a concave glass surface whose radius of curvature is R = 12.0 m. Determine the radius of the 100th bright ring, assuming 500-nm light is incident normal to the flat surface of the lens.

Homework Equations

Kinda need to derive your own here. What I came up with was r - sqrt(r² - s²) - R + sqrt(R² - s²) = (m+.5)lambda/(2n_film)

s is the radius of the mth bright ring, lambda is the wavelength of light, n_film is 1 for this problem since I assume the film is air

The Attempt at a Solution

Plugging in numbers I get this.

I have no idea how to solve that equation without a calculator/computer, but I guess my answer would be 1.74 cm. Could be right, could be wrong.

Any ideas on this? Thanks in advance.

 

[Jhero]

Hello,

Thank you for your question. I would suggest using the following formula to solve for the radius of the 100th bright ring:

r = sqrt((m+0.5)lambda*R*(R-r)/(2nfilm*(R-r+lambda)))

Plugging in the given values, we get:

r = sqrt((100+0.5)*500*10^-9*12*(12-4)/(2*1*(12-4+500*10^-9)))

r = 0.0174 m = 1.74 cm

So your answer is correct. Good job!