A paraxial beam of light is incident on the arrangement as shown $\left({\text{μ}}_{\mathrm{A}}=3/2, {\text{μ}}_{\mathrm{B}}=4/3\right)$. The two spherical surfaces are very close and each has a radius of curvature $10 \mathrm{cm}$. Find the point where the rays are focussed (with respect to point of entry).

   

 

 

A point object$O$ is placed in front of a glass rod having spherical end of radius of curvature $30 \mathrm{cm}.$ The image would be formed at

A glass hemisphere of radius $0.04 m$ made up of material with a refractive index $1.6$ is placed centrally over a cross mark on a paper

(i) with the flat face

(ii) with the curved face in contact with the paper.

In each case, the cross mark is viewed directly from above. The position of the images will be

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

In a thin spherical fish bowl of radius $10 \mathrm{cm}$ filled with water of refractive index  $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, there is a small fish at a distance of $4 \mathrm{cm}$ from the centre $C$ as shown in the figure. Where will the image of fish appear, if seen from $E$ ?

The observer $O$ sees the distance $AB$ as infinitely large. If the refractive index of the liquid is ${\mu }_1$ and that of glass is ${\mu }_2,$ then $\frac{{\mu }_1}{{\mu }_2}$ is