The refractive indices of medium $(1)$ and medium $(2)$ are $\eta_{1}$ and $\eta_{2}$ respectively,and the velocities of light in these media are $v_{1}$ and $v_{2}$ respectively. What is the formula to find the refractive index of medium $(2)$ with respect to medium $(1)$,denoted as $\eta_{21}$?

The figure below shows an object $AB$ placed on the principal axis of a convex lens placed in air. $F_{1}$ and $F_{2}$ are the two foci of the lens. Copy the diagram.
$(i)$ Draw a ray of light starting from $B$ and passing through $O$. Show the same ray after refraction by the lens.
$(ii)$ Draw another ray from $B$ which passes through $F_{2}$ after refraction by the lens.
$(iii)$ Locate the final image formed.
$(iv)$ Is the image real or virtual?

Draw a ray diagram showing the path of rays of light when it enters with oblique incidence: $(i)$ from air into water; $(ii)$ from water into air.

The image formed by a concave mirror is observed to be virtual,erect and larger than the object. Then the position of the object should be

Discuss the position and nature of the image formed by a concave mirror when the object is moved from infinity towards the pole of the mirror.

Through which point of a convex lens does a ray of light pass without undergoing refraction?