$A$ candle of height $3 \ cm$ is placed at $300 \ cm$ from a wall. $A$ concave mirror is kept at a distance $x$ from the wall in such a way that the image of the flame on the wall is $9 \ cm$. Then $x$ is $.... \ cm$.

For a concave mirror,the minimum distance between a real object and its real image is ...........

The direction of a ray of light incident on a concave mirror is shown by $PQ$,while the directions in which the ray would travel after reflection are shown by four rays marked $1, 2, 3,$ and $4$. Which of the four rays correctly shows the direction of the reflected ray?

Suppose while sitting in a parked car,you notice a jogger approaching towards you in the side view mirror of radius of curvature $R = 2 \; m$. If the jogger is running at a speed of $5 \; m s^{-1}$,how fast does the image of the jogger appear to move when the jogger is $(a) \; 39 \; m$,$(b) \; 29 \; m$,$(c) \; 19 \; m$,and $(d) \; 9 \; m$ away?

The distance between an object and its image (magnified by $-\frac{1}{3}$) is $30 \ cm$. The focal length of the mirror used is $\left(\frac{x}{4}\right) \ cm$,where the magnitude of the value of $x$ is . . . . . . .

Provide the object and image distances,type,size,and magnification for an object placed in front of a concave spherical mirror for the cases shown in the image.