A man inside a spherical diving bell watches a fish through a window in the bell, as in the figure below. If the diving bell has radius $R=1\mathrm{.}74m$ and the fish is a distance $p=1\mathrm{.}38m$ from the window, calculate the image distance and the magnification. Neglect the thickness of the window. $($Use $1\mathrm{.}333$ and $1\mathrm{.}000$ for the indices of refraction of water and air, respectively.$)$

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$($a$)$ the image distance $($in m $)$

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$($b$)$ the magnification