The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of the cornea $(7.8 \, mm)$. This surface separates two media of refractive indices $1$ and $1.34$. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus in $cm$.

$A$ 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 $A$.

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

Two transparent media having refractive indices $1.0$ and $1.5$ are separated by a spherical refracting surface of radius of curvature $30\,cm$. The centre of curvature of the surface is towards the denser medium and a point object is placed on the principal axis in the rarer medium at a distance of $15\,cm$ from the pole of the surface. The distance of the image from the pole of the surface is .......$cm$.

$A$ 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 $\,cm$)

The given figure shows a ray of light passing through two media having refractive indices $4/3$ and $3/2$ respectively. The ratio of times taken by the ray in traversing the distances $AB$ and $BC$ is