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## Homework Statement

A biconvex lens of refractive index ##n## and radius of curvature ##r## and focal length ##f## floats horizontally on liquid mercury such that its lower surface is effectively a spherical mirror. A point object on the optical axis a distance ##u## away is then found to coincide with its image. What are ##r## and ##n##?

## Homework Equations

The previous half of the equation made us derive ## \frac{n_2}{v} + \frac{n_1}{u} = \frac{n_2-n_1}{r} ## for a spherical interface of radius ##r## separating 2 different media. I don't know if this would be useful here?

Also have ## \frac{2}{u} = \frac{1}{f} ##

I believe we can't use the lens maker's equation in this circumstance?

## The Attempt at a Solution

Deriving the relations above.