$A$ convergent beam of light is incident on a convex mirror so as to converge to a distance $12 \, cm$ from the pole of the mirror. An inverted image of the same size is formed coincident with the virtual object. What is the focal length of the mirror? $(cm)$

Assertion : $A$ point object is placed at a distance of $26 \ cm$ from a convex mirror of focal length $26 \ cm$. The image will not form at infinity.
Reason : For the above-given system,the equation $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ gives $v = \infty$.

$A$ concave mirror of radius of curvature $R$ has a circular outline of radius $r$. $A$ circular disc is to be placed normal to the axis at the focus,so that it collects all the light that is reflected from the mirror from a beam parallel to the axis. For $r \ll R$,the area of this disc has to be at least

$A$ driver sitting inside a parked car is watching vehicles approaching from behind with the help of a side-view mirror,which is a convex mirror with a radius of curvature $R = 2 \ m$. Another car approaches from behind with a uniform speed of $90 \ km/h$. When the car is at a distance of $24 \ m$ from the mirror,the magnitude of the acceleration of the image in the side-view mirror is $a$. The value of $100a$ is $m/s^2$.

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

If $x$ is the distance of an object from the focus of a concave mirror and $y$ is the distance of the image from the focus, then which of the following graphs is correct between $x$ and $y$?