Phy que 13.

Solution,
For the image of the object to form at the same place as the object is, the rays from the object after refraction from the first curved surface become parallel to the principal axis of the curved reflecting surface such that it falls on the glass plate perpendicularly.
This means that the image distance, v, after refraction from the first curved plane must be infinite.

Applying the mirror equation for spherical mirrors:
$$\begin{gathered} \frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R} \\ where, \\ u = -30 cm \\ v = \infty \\ {\mu }_2=refractive index of the glass = 1.5 \\ {\mu }_1=refractive index of air=1 \\ So, \\ \frac{1.5}{\infty }-\frac{1}{-30}=\frac{1.5-1}{R} \\ \frac{1}{30}=\frac{1}{2R} \\ R=15cm \end{gathered}$$