b
For image to form at object itself, says must retrace their path back to object. Hence must incident on mirror normally.

case \(1\) : Object will be at focus of lens

\(\frac{1}{f}=(\mu-1)\left(\frac{1}{R}-\frac{1}{-R}\right)=\frac{1}{-18}\)

\(\Rightarrow {\mathrm{R}}=18\, \mathrm{cm}\)

case \(2\) :  Retraction at \(1^{\text {st }}\) surface:

\(\frac{1}{-27}-\frac{1.5}{V_{1}}=\frac{1-1.5}{R}\)  ..... \((i)\)

\(2^{\text {nd }}\) retraction:

\(\frac{1.5}{V_{1}}-\frac{\mu}{\infty}=\frac{1.5-u}{-R}\)  ..... \((ii)\)

From \((i)\) and \((ii)\)

\(\mu=\frac{4}{3}\)