$A$ point object is placed at the center of a glass sphere of radius $6 \ cm$ and refractive index $1.5$. The distance of the virtual image from the surface of the sphere is.......$cm$

$A$ luminous point object $O$ is placed at a distance $2R$ from the spherical boundary separating two transparent media of refractive indices $n_1$ and $n_2$ as shown,where $R$ is the radius of curvature of the spherical surface. If $n_1 = \frac{4}{3}$,$n_2 = \frac{3}{2}$ and $R = 10 \text{ cm}$,the image is obtained at a distance from $P$ equal to:

$A$ curved surface of radius $R$ separates two media of refractive indices $\mu_1$ and $\mu_2$ as shown in figures $A$ and $B$. Choose the correct statement$(s)$ related to the real image formed by the object $O$ placed at a distance $x$,as shown in figure $A$.

Parallel rays are incident on a transparent sphere along its one diameter. After refraction,these rays converge at the other end of this diameter. The refractive index of the sphere is:

Light from a point source in air falls on a spherical glass surface (refractive index,$\mu=1.5$ and radius of curvature $=50\ cm$). The image is formed at a distance of $200\ cm$ from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is . . . . . . $m$.

$A$ small object is embedded in a glass sphere $(\mu = 1.5)$ of radius $5.0\, cm$ at a distance $1.5\, cm$ to the left of the centre. Locate the image of the object as seen by an observer standing to the left of the sphere.