What is the focal length of this curved surface in $cm$?

$A$ spherical surface of radius of curvature $R$ separates air (refractive index $n_1 = 1.0$) from glass (refractive index $n_2 = 1.5$). The center of curvature is inside the glass. $A$ point object placed at $P$ forms a real image at $Q$. The line $PQ$ intersects the surface at $O$ and $PO = OQ$. The distance $PO$ is:

Light from a point source in air falls on a spherical glass surface ($n = 1.5$ and radius of curvature $= 20\; cm$). The distance of the light source from the glass surface is $100\; cm$. At what position (in $cm$) the image is formed?

$A$ transparent thin film of uniform thickness and refractive index $n_1=1.4$ is coated on the convex spherical surface of radius $R$ at one end of a long solid glass cylinder of refractive index $n_2=1.5$,as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance $f_1$ from the film,while rays of light traversing from glass to air get focused at distance $f_2$ from the film. Then:
$(A)$ $|f_1|=3R$
$(B)$ $|f_1|=2.8R$
$(C)$ $|f_2|=2R$
$(D)$ $|f_2|=1.4R$

$A$ clear transparent glass sphere $(\mu=1.5)$ of radius $R$ is immersed in a liquid of refractive index $1.25$. $A$ parallel beam of light incident on it will converge to a point. The distance of this point from the center will be

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