Where should an object $6 \mathrm{cm}$ long be placed in front of a convex mirror of focal length $60 \mathrm{cm}$ to obtain an image $2 \mathrm{cm}$ long.

A mirror is placed at an angled of $30°$ with respect to $y-$axis (see figure). A light ray travelling in the negative $y-$direction strikes the mirror. The direction of the reflected ray is given by the vector

A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6 cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen :

A point object is moving uniformly towards the pole of a concave mirror of focal length $25 \mathrm{cm}$ along its axis as shown below. The speed of the object is $1 {\mathrm{ms}}^{-1}$. At $t=0$, the distance of the object from the mirror is $50 \mathrm{cm}$. The average velocity of the image formed by the mirror between time $t=0$ and $t=0.25 \mathrm{s}$ is:

A point source of light, $S$ is placed at a distance $L$ in front of the center of plane mirror of width $d$ which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance $2L$ as shown below. The distance over which the man can see the image of the light source in the mirror is:

A particle is oscillating on the $x$-axis with an amplitude $2 \mathrm{cm}$ about the point $x_0=10 \mathrm{cm}$ with a frequency. A concave mirror of focal length $5 \mathrm{cm}$ is placed at the origin (see figure).

Identify the correct statements?
(i) The image executes periodic motion.
(ii) The image executes non-periodic motion.
(iii) The turning points of the image are asymmetric with respect to the image of the point at $X=10 \mathrm{cm}$.
(iv) The distance between the turning points of the oscillation of the image is $\frac{100}{21}\mathrm{ }\mathrm{cm}$.