What is the power of a concave lens of focal length $25\, cm$?

Which type of mirror can produce a virtual image?

Magnification produced by a rear-view mirror fitted in vehicles $....$

$A$ convex lens forms a real and inverted image of a needle at a distance of $50\, cm$ from the lens. Where should the needle be placed in front of the convex lens so that this image is of the same size as the object? Also, find the power of the lens.

Identify the device used as a spherical mirror or lens in the following cases,where the image formed is virtual and erect in each case.
$(a)$ Object is placed between the device and its focus,image formed is enlarged and behind it.
$(b)$ Object is placed between the focus and the device,image formed is enlarged and on the same side as that of the object.
$(c)$ Object is placed between infinity and the device,image formed is diminished and between the focus and optical centre on the same side as that of the object.
$(d)$ Object is placed between infinity and the device,image formed is diminished and between the pole and focus,behind it.

$A$ plane mirror is placed vertically facing due north. An arrow pointing north-east is kept in front of the mirror. In which direction will the arrow point in this image?