$A$ point object $O$ is placed in front of a glass rod having a spherical end of radius of curvature $30\; cm$ as shown in the figure. The image would be formed at:

$A$ quarter cylinder of radius $R$ and refractive index $1.5$ is placed on a table. $A$ point object $P$ is kept at a distance of $mR$ from it. Find the value of $m$ for which a ray from $P$ will emerge parallel to the table as shown in the figure.

$A$ laser beam falls on a crystal ball of radius $R$ as shown in the figure. What is its refractive index?

$A$ 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:

Two concave refracting surfaces of equal radii of curvature $R$ and refractive index $1.5$ face each other in air as shown in the figure. $A$ point object $O$ is placed midway between $P$ and $B$. The separation between the images of $O$ formed by each refracting surface is: (in $R$)

$A$ convex refracting surface of radius of curvature $20 \, cm$ separates two media of refractive indices $\frac{4}{3}$ and $1.6$. An object is placed in the first medium $(\mu = 4/3)$ at a distance of $200 \, cm$ from the refracting surface. The position of the image formed is.....$cm$