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

$A$ parallel beam of light travelling in water (refractive index $\mu_1 = 4/3$) is refracted by a spherical air bubble of radius $R = 2 \, cm$ situated in water. Assuming the light rays to be paraxial,the position of the image due to refraction at the first surface is:

$A$ curved surface of radius $R$ separates two media of refractive indices $\mu_1$ and $\mu_2$ as shown in figures $A$ and $B$. Choose the correct statement$(s)$ related to the real image formed by the object $O$ placed at a distance $x$,as shown in figure $A$.

$A$ 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 $\,cm$)

$A$ point object is placed at the centre of a glass sphere of radius $6 \, cm$ and refractive index $1.5$. The distance of the virtual image from the surface of the sphere is.....$cm$

Region $I$ and $II$ are separated by a spherical surface of radius $25\, \text{cm}$. An object is kept in region $I$ at a distance of $40\, \text{cm}$ from the surface. The distance of the image from the surface is $.....\, \text{cm}$.