An object is at a distance $x_1$ from the focus of a concave mirror,and its image is formed at a distance $x_2$ from the focus. The focal length of the mirror is:

The distance of a real object from the focus of a convex mirror of radius of curvature $a$ is $b$. Then the distance of the image from the focus is

$A$ boy stands $30 \,cm$ in front of a mirror. The height of his erect image is $1/5 \,th$ of his actual height. The mirror used is ..... .

For a concave mirror,the $\frac{1}{u}$ versus $\frac{1}{v}$ graph obtained by the parallax method is as shown in the figure. The graph is a straight line with a slope of $-1$. The estimated value of the focal length of the mirror is: (in $cm$)

$A$ small candle,$2.5\; cm$ in size,is placed at $27\; cm$ in front of a concave mirror of radius of curvature $36\; cm$. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror,how would the screen have to be moved?

Let the transverse magnification produced by a spherical mirror be $m$. Then,for the same position of the object,the longitudinal magnification will be: