$(a)$ $A$ concave mirror produces a three times enlarged real image of an object placed at $10\, cm$ in front of it. Calculate the focal length of the mirror.
$(b)$ Show the formation of the image with the help of a ray diagram when an object is placed $6\, cm$ away from the pole of a convex mirror.

An object $3.0 \text{ cm}$ high is placed perpendicular to the principal axis of a concave lens of focal length $7.5 \text{ cm}$. The image is formed at a distance of $5.0 \text{ cm}$ from the lens. Calculate $(i)$ distance at which object is placed,and $(ii)$ size and nature of image formed.

Identify the device used as a spherical mirror or lens in the following cases,where the image formed is virtual and erect in each case.
$(a)$ Object is placed between the device and its focus,image formed is enlarged and behind it.
$(b)$ Object is placed between the focus and the device,image formed is enlarged and on the same side as that of the object.
$(c)$ Object is placed between infinity and the device,image formed is diminished and between the focus and optical centre on the same side as that of the object.
$(d)$ Object is placed between infinity and the device,image formed is diminished and between the pole and focus,behind it.

$A$ beam of light incident on a plane mirror forms a real image on reflection. The incident beam is

$A$ concave lens made of a material of refractive index $n_{1}$ is kept in a medium of refractive index $n_{2}$. $A$ parallel beam of light is incident on the lens. Complete the path of rays of light emerging from the concave lens if
$(i)$ $n_{1} > n_{2}$ $(ii)$ $n_{1}=n_{2}$ $(iii)$ $n_{1} < n_{2}$

Where will the image be formed by a concave mirror when an object is placed between the pole and the focus point of the mirror?