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 enclosed in a transparent solid sphere of radius $8 \ cm$. The object is situated at $2 \ cm$ from the centre of the sphere. If its image appears to be at $3.2 \ cm$ from the nearest side,then the refractive index of the material of the sphere is:

$A$ narrow parallel beam of light is incident paraxially on a solid transparent sphere of radius $r$ kept in air. What should be the refractive index if the beam is to be focused at the farther surface of the sphere?

The given figure shows a ray of light passing through two media having refractive indices $4/3$ and $3/2$ respectively. The ratio of times taken by the ray in traversing the distances $AB$ and $BC$ is

Two transparent media having refractive indices $1.0$ and $1.5$ are separated by a spherical refracting surface of radius of curvature $30\,cm$. The centre of curvature of the surface is towards the denser medium and a point object is placed on the principal axis in the rarer medium at a distance of $15\,cm$ from the pole of the surface. The distance of the image from the pole of the surface is .......$cm$.

$A$ point object is placed at the centre 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.....$cm$