What is the relation between the radius of curvature $(R)$ and the focal length $(f)$ of a spherical mirror?

An object is placed at a distance of $40\, cm$ in front of a concave mirror of focal length $20\, cm$. The image produced is

$A$ concave mirror and a convex lens are held in water. What changes, if any, do you expect in their focal length?

Where should an object be placed in front of a convex lens to form a real,inverted,and same size image?

One half of a convex lens is covered with a black paper.
$(a)$ Show the formation of the image of an object placed at $2F_{1}$ of such a covered lens with the help of a ray diagram. Mention the position and nature of the image.
$(b)$ Draw the ray diagram for the same object at the same position in front of the same lens,but now uncovered. Will there be any difference in the image obtained in the two cases? Give a reason for your answer.

Draw a labelled ray diagram to locate the image of an object formed by a convex lens of focal length $20 \, cm$ when the object is placed $30 \, cm$ away from the lens.