In a medium of refractive index $1.6$ having a convex surface,a point object is placed at a distance of $12 \,cm$ from the pole. The radius of curvature of the surface is $6 \,cm$. Locate the image as seen from air.

$A$ spherical glass is attached to a rigid wall as shown in the figure. An observer located at point $O$ is looking at a point $A$ on the wall. The refractive index of the glass is $1.5$ and that of air is $1.0$. The distances are $OA = 8 \text{ cm}$, $XA = 3 \text{ cm}$. If the radius of curvature of the spherical glass surface is $R = 5 \text{ cm}$, then the apparent distance of $A$ from the observer $O$ is (in $\text{ cm}$)

$A$ parallel beam of light travelling in air (refractive index $1.0$) is incident on a convex spherical glass surface of radius of curvature $50 \ cm$. The refractive index of glass is $1.5$. The rays converge to a point at a distance $x \ cm$ from the centre of curvature of the spherical surface. The value of $x$ is . . . . . . $cm$.

$A$ parallel beam of light is allowed to fall on a transparent spherical globe of diameter $30 \,cm$ and refractive index $1.5$. The distance from the centre of the globe at which the beam of light can converge is . . . . . . $mm$.

As shown in the figure,region $BCDEF$ and $ABFG$ have refractive indices $2.0$ and $1.5$ respectively. $A$ particle $O$ is kept at the midpoint of region $BCEF$. The final image of the object as seen by the eye is at a distance of:

$A$ concave spherical refracting surface separates two media,glass and air $(\mu_1 = 1.5, \mu_2 = 1.0)$. If the image is to be real,at what minimum distance $u$ should the object be placed in the glass if $R$ is the radius of curvature?