The image formed by a convex spherical mirror is always:

$(a)$ State the relation between object distance,image distance and the focal length of a spherical mirror.
$(b)$ Draw a ray diagram to show the image formed by a concave mirror when an object is placed between the pole and focus of the mirror.
$(c)$ $A$ concave mirror of focal length $15\, cm$ forms an image of an object kept at a distance of $10\, cm$ from the mirror. Find the position,nature and size of the image formed by it.

If the focal length of a spherical mirror is $20 \ cm$,what is its radius of curvature (in $cm$)?

$(i)$ Under what condition does a concave mirror produce a virtual and magnified image? Draw a labelled ray diagram to show the formation of the image in the above case. Also,state the position of the object to produce a magnified and real image.
$(ii)$ $A$ ray of light moving along the principal axis is falling on a concave mirror. Draw the path of the reflected ray. Also,state the values of the angle of incidence and reflection in this case.

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.

$A$ diminished virtual image can be obtained only in