An object $1 \, cm$ tall is placed at a distance of $15 \, cm$ from a concave mirror of focal length $10 \, cm$. Find the position,size,and nature of the image formed.

An object is placed $50\, cm$ from a lens that produces a virtual image at a distance of $10\, cm$ in front of the lens. Calculate the focal length of the lens. (in $, cm$)

For what position of the object does a convex lens form an erect and virtual image?

The following table gives the values of refractive indices of a few media:

$S.No.$	$1$	$2$	$3$	$4$	$5$
Medium	Water	Crown glass	Rock salt	Ruby	Diamond
Refractive index	$1.33$	$1.52$	$1.54$	$1.71$	$2.42$

Use this table to give an example of $(i)$ a medium pair so that light speeds up when it goes from one of these media to another. $(ii)$ a medium pair so that light slows down when it goes from one of these media to another.

The figure below shows an object $AB$ placed on the principal axis of a lens $L$. The two foci of the lens are $F_1$ and $F_2$. The image formed by the lens is erect,virtual and diminished. Copy the diagram and answer the following questions: $(i)$ Draw the outline of the lens $(L)$ used. $(ii)$ Draw a ray from $B$ passing through $O$. Show the ray after refraction by the lens. $(iii)$ Draw a ray of light starting from $B$,which after passing parallel to the principal axis,is incident on the lens and emerges after refraction from it. $(iv)$ Locate the final image formed.

Define lateral magnification.