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

If the image formed by a mirror for all positions of the object placed in front of it is always erect and diminished,what type of mirror is it? Draw a ray diagram to justify your answer. Where and why do we generally use this type of mirror?

$A$ ray of light $XY$ is incident on a spherical mirror as shown in the diagram. Redraw the diagram and mark the normal,angle of incidence and angle of reflection.

$A$ convex lens of focal length $10 \ cm$ is placed at a distance of $12 \ cm$ from a wall. How far from the lens should an object be placed so as to form its real image on the wall (in $cm$)?

With respect to air,the refractive indices of ice and rock salt are $1.31$ and $1.54$ respectively. Calculate the refractive index of rock salt with respect to ice.

Name the type of lens that can be used as a magnifying glass. Give reason$(s)$ and draw a ray diagram to support your answer.