Where is the image formed when an object is placed at the principal focus $(F)$ in front of a convex lens?

If an object of $4 \, cm$ height is placed at a distance of $12 \, cm$ from a concave mirror,then its image is formed at a distance of $24 \, cm$ from the mirror and behind it. What will be the height of the image (in $, cm$)?

The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. If the image is three times the size of the flame and the distance between the lens and the image is $80 \, cm$,at what distance should the candle be placed from the lens? What is the nature of the image at a distance of $80 \, cm$ from the lens (in $, cm$)?

In a diagram,show the following for both a convex mirror and a concave mirror:
$(i)$ Principal axis
$(ii)$ Pole
$(iii)$ Focus
$(iv)$ Centre of curvature
$(v)$ Radius of curvature

The velocity of light in air is $3 \times 10^{8} \, m \, s^{-1}$. What is the velocity of light in water? (The absolute refractive index of water is $\frac{4}{3}$.)

$A$ convex mirror used on an automobile has $3\, m$ radius of curvature. If a bus is located at $5\, m$ from this mirror,find the position,nature,and size of the image.