Why does a ray of light passing through the centre of curvature of a concave mirror gets reflected along same path after reflection?

It is desired to obtain an erect image of an object, using concave mirror of focal length of 12cm.
Will the image be smaller or larger than the object? Draw ray diagram to show the formation of image in this case.

List four specific characteristics of the images of the objects formed by convex mirrors.

When an object is placed at a distance of 15cm from a concave mirror, its image is formed at 10cm in front of the mirror. Calculate the focal length of the mirror.

A lens is cut into two equal halves: Along the principal axis.
What will be the focallength of each half?

Explain with the help of a diagram, why a pencil partly immersed in water appears to be bent at the water surface.

With the help of a labelled diagram explain how a convex lens converges a beam of parallel light rays.

An object is placed at a distance of 30cm in front of a convex mirror of focal length 15cm. Write four characteristics of the image formed by the mirror.

An object is placed at the following distance from a convex lens of focal length 15cm:

1. 35cm
2. 30cm
3. 20cm
4. 10cm

Which position of the object will produce:

1. A magnified real image?
2. A magnified virtual image?
3. A diminished real image?
4. An image of same size as the object?

An object lies at a distance of 2f from a concave lens of focal length f. Draw a ray-diagram to illustrate the image formation.