An object is placed at the principal focus of a convex mirror. The image will be at

In an experiment to determine the focal length $(f)$ of a concave mirror by the parallax method,a student places the object pin $\text{A}$ on the principal axis at a distance $x$ from the pole $\text{P}$. The student looks at the pin and its inverted image from a distance,keeping his/her eye in line with $\text{PA}$. When the student shifts his/her eye towards the left,the image appears to the right of the pin. Then:

The ratio of the diameter of the sun to the distance between the earth and the sun is approximately $0.009$. The approximate diameter of the image of the sun formed by a concave spherical mirror of radius of curvature $0.4 \ m$ is

$A$ straight line joining the object point and image point is always perpendicular to the mirror:

An object and a concave mirror of focal length $f=10 \text{ cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_0=15 \text{ cm s}^{-1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by $u$. When $u=30 \text{ cm}$,the speed of the mirror $V_m$ is such that the image is instantaneously at rest with respect to the laboratory frame,and the object forms a real image. The magnitude of $V_m$ is . . . . . $\text{cm s}^{-1}$.

At what distance from a concave mirror of focal length $10 \, cm$ should an object be placed to get a magnification of $2$?