What is meant by a lateral shift?

What is the nature of the image formed by an object placed at a distance of $10 \text{ cm}$ in front of a concave mirror with a focal length of $20 \text{ cm}$?

Where should an object be placed in front of a concave mirror to obtain its image at the same position?

$A$ pencil when dipped in water in a glass tumbler appears to be bent at the interface of air and water. Will the pencil appear to be bent to the same extent,if instead of water we use liquids like kerosene or turpentine? Support your answer with reason.

$(a)$ Define the optical centre of a spherical lens.
$(b)$ You are given a convex lens of focal length $30 \, cm$. Where would you place an object to get a real,inverted,and highly enlarged image of the object? Draw a ray diagram showing the image formation.
$(c)$ $A$ concave lens has a focal length of $20 \, cm$. At what distance from the lens should an object be placed so that it forms an image at $15 \, cm$ away from the lens?

How can you identify the three types of mirrors without touching them?