An object placed in front of a concave mirror at a distance of $x \ cm$ from the pole gives a $3$ times magnified real image. If it is moved to a distance of $(x+5) \ cm$, the magnification of the image becomes $2$. The focal length of the mirror is: (in $cm$)

Incident parallel rays make an angle of $5^{\circ}$ with the axis of a concave mirror of focal length $20 \ cm$. The perpendicular distance of the image from the axis is nearly $-$ (in $cm$)

While using an electric bulb for street lighting, the reflector should be a:

The focal length of a concave mirror is $50 \, cm$. Where should an object be placed so that its image is two times magnified and inverted?

Use the mirror equation to deduce that:
$(a)$ an object placed between $f$ and $2f$ of a concave mirror produces a real image beyond $2f$.
$(b)$ a convex mirror always produces a virtual image independent of the location of the object.
$(c)$ the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.
$(d)$ an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.

$A$ point object is placed at a distance of $10 \ cm$ and its real image is formed at a distance of $20 \ cm$ from a concave mirror. If the object is moved by $0.1 \ cm$ towards the mirror,the image will shift by about: