Two transparent media having refractive indices 1 . 0 and 1 . 5 are...

Let's consider the following diagram-

The relation between the object distance, the image distance and the radius of curvature of the spherical surface can be written as

$\dfrac{{\mu}_{2}}{v} - \dfrac{{\mu}_{1}}{u} = \dfrac{{\mu}_{2} - {\mu}_{1}}{R} . . . \left(1\right)$

Substitute the values of the known parameters into equation (1) and solve to calculate the required image distance.

$\begin{cases}\dfrac{1 . 5}{v} - \dfrac{1}{- 15} & = & \dfrac{1 . 5 - 1 . 0}{30} \\ & ⇒ & \dfrac{1 . 5}{v} = \dfrac{1}{60} - \dfrac{1}{15} \\ & = & - \dfrac{1}{20} \\ & ⇒ & v = - 30\end{cases}$

Hence, the image is formed at a distance of $30cm$ from the pole on the same direction as the object is placed.