$A$ spherical convex surface of power $5 \text{ dioptre}$ separates object and image space of refractive indices $1.0$ and $\frac{4}{3}$ respectively. The radius of curvature of the surface is (in $\text{ cm}$)

$A$ small object is placed in the air, at a distance of $45 \,cm$ from a convex refracting surface of radius of curvature $15 \,cm$. If the surface separates air from glass of refractive index $1.5$, then the position of the image is: (in $\,cm$)

Two refracting media are separated by a spherical interface as shown in the figure. $PP'$ is the principal axis, $\mu_1$ and $\mu_2$ are the refractive indices of the medium of incidence and the medium of refraction respectively. Then:

An air bubble in a glass sphere having a $4 \,cm$ diameter appears $1 \,cm$ from the surface nearest to the eye when looked at along the diameter. If the refractive index of glass is $_a\mu_g = 1.5$,the actual distance of the bubble from the refracting surface is.....$cm$.

$A$ denser medium of refractive index $1.5$ has a concave surface of radius of curvature $12 \, cm$. An object is situated in the denser medium at a distance of $9 \, cm$ from the pole. Locate the image due to refraction in air.

The slab of a material of refractive index $2$ shown in the figure has a curved surface $APB$ of radius of curvature $10 \, cm$ and a plane surface $CD$. On the left of $APB$ is air and on the right of $CD$ is water with refractive indices as given in the figure. An object $O$ is placed at a distance of $15 \, cm$ from the pole $P$ as shown. The distance of the final image of $O$ from $P$,as viewed from the left,is ..... $cm$.