Newton\'s rings are observed when a plano-convex lens is placed convex side down

Question

Newton's rings are observed when a plano-convex lens is placed convex side down on a plane glass surface and the system is illuminated from above with monochromatic light. The radius of the first bright ring is 1 mm.
(a) If the radius of the convex surface is 4 m, what is the wavelength of the light used?
(b) If the space between the lens and at glass surface is lled with water, what is the radius of therst bright ring?

I didn't have a problem with (a) I used equation lambda=x^2/(m+1/2)R where x is the radius of the bright ring and R is the radius of curvature

I don't know how to do b, i cant find an equation for newtons rings that incorporates refractive index. Thanks

Explanation / Answer

x = 1 mm. (a) If the radius of the convex surface is R = 4 m, what is the wavelength of the light used? lambda = x^2/(m+1/2)R = x^2/(0.5R) = 500 nm (b) If the space between the lens and at glass surface is filled with water, what is the radius of the 1st bright ring? n = 1.33, so now lambda in water = 500 nm, in air lambda = 500*1.33 = 665 nm use lambda = x'^2/(0.5R) x' = sqrt(lambda*0.5R) = sqrt(665 nm * 2 m) = 1.15 nm

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