$A$ point object is placed at a distance of $15 \, cm$ from a glass rod with a spherical end. The radius of curvature of the spherical end is $30 \, cm$. Find the position of the image formed.

$A$ point source of light at the surface of a sphere causes a parallel beam of light to emerge from the opposite surface of the sphere. The refractive index of the material of the sphere is

$A$ spherical surface of radius of curvature $10\,cm$ separates two media $X$ and $Y$ of refractive indices $3/2$ and $4/3$ respectively. The centre of the spherical surface lies in the denser medium. An object is placed in medium $X$. For the image to be real,the object distance must be:

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 convex curved surface of radius $20 \,cm$ and refractive index $1.5$. If the source is located at $100 \,cm$ from the convex surface,the image will be formed at what distance from the object?

$A$ spherical surface separates two media of refractive indices $1$ and $1.5$ as shown in the figure. Find the distance of the image of an object $O$ from the spherical surface. ($C$ is the center of curvature of the spherical surface and $R$ is the radius of curvature).