Explain formation of images by convex and concave mirrors for different object position. Show the size, position and nature of image by ray diagrams.

A spherical mirror is obtained as shown in the figure from a hollow glass sphere, if an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object? (Figure down as schematic and not to scale)

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 $\frac{100}{21}\mathrm{ }\mathrm{cm}$.

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 $5 \mathrm{cm}$ long object is placed in front of a concave mirror of radius of curvature $40 \mathrm{cm}$. The distance of object from mirror is $40 \mathrm{cm}$. Find the distance and size of the image.

An object '$O$' is placed at a distance of $100 \mathrm{cm}$ in front of a concave mirror of radius of curvature $200 \mathrm{cm}$ as shown in the figure. The object starts moving towards the mirror at a speed $2 \mathrm{cm} {\mathrm{s}}^{-1}$. The position of the image from the mirror after $10 \mathrm{s}$ will be at _____ $\mathrm{cm}$.