Please show any necessary calculations, thanks! Determining the index of refract

Question

Please show any necessary calculations, thanks!

Determining the index of refraction of a liquid A liquid's index of refraction can be determined with the following method. A double convex lens of known focal length f and radii of curvature plusminus R? is brought near a flat glass plate, and a drop of the liquid in question is put between the lens and the plate. The liquid thus assumes the shape of a planoconcave lens with radius of curvature -R. If the focal length of the combination of the two lenses is measured to be f', show that the liquid's index of refraction is n = R(1/f - 1/f') + 1.

Explanation / Answer

Focal length f , of double convex length of radii +/-R, is given by
1/f = (ng - 1) (2/R) ........1
where ng is Index of refraction of glass.
Focal length fl of Planoconcave lens, formed by liquid between convex lens and plate, is given by
1/fl = (n-1) (- 1/R) ........2
n is Index of refraction of liquid
Focal length of combination f' is given by
1/f' = 1/f + 1/fl
Using value of fl fromeuation 2 we get
1/f' = 1/f +  (n-1) (- 1/R)
   = 1/f - n/R +R
n/R = 1/f - 1/f' + R
n = R ( 1/f - 1/f') +1

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