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SERCP$1125\mathrm{.}3.$P$\mathrm{.}022.$

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When a drop of water is placed on a flat, clear surface such as a glass slide or plastic sheet, surface tension pulls the top surface into a curved, lens$-$like shape so that the drop functions as a simple magnifier. Suppose a drop of water has a maximum angular magnification of $3\mathrm{.}23.($Use $1\mathrm{.}333$ for the index of refraction for water.$)$

$($a$)$ Find the drop's focal length in cm $.$

$$ cm

$($b$)$ Assuming the bottom surface of the drop is flat, use the lens$-$maker's equation from Topic $23$ to calculate the radius of curvature $($in cm $)$ of the top surface.

$$ cm

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