An object is placed at the following distances from a concave mirror of focal length $15 \, cm$.
$(a)$ $10 \, cm$ $(b)$ $20 \, cm$ $(c)$ $30 \, cm$ $(d)$ $40 \, cm$
Which position of the object will produce:
$(1)$ Virtual image
$(2)$ $A$ diminished real image
$(3)$ An enlarged real image
$(4)$ An image of same size

(A-10, B-20, C-30, D-40) For a concave mirror with focal length $f = 15 \, cm$:
$(1)$ $A$ virtual image is formed when the object is placed between the pole and the focus $(u < 15 \, cm)$. Thus,the position is $10 \, cm$.
$(2)$ $A$ diminished real image is formed when the object is placed beyond the center of curvature $(u > 30 \, cm)$. Thus,the position is $40 \, cm$.
$(3)$ An enlarged real image is formed when the object is placed between the focus and the center of curvature $(15 \, cm < u < 30 \, cm)$. Thus,the position is $20 \, cm$.
$(4)$ An image of the same size is formed when the object is placed at the center of curvature $(u = 2R = 30 \, cm)$. Thus,the position is $30 \, cm$.