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

$A$ concave lens made of a material of refractive index $n_{1}$ is kept in a medium of refractive index $n_{2}$. $A$ parallel beam of light is incident on the lens. Complete the path of rays of light emerging from the concave lens if
$(i)$ $n_{1} > n_{2}$ $(ii)$ $n_{1}=n_{2}$ $(iii)$ $n_{1} < n_{2}$

$(a)$ $A$ converging lens forms a real and inverted image of an object at a distance of $100 \, cm$ from it. Where should an object be placed in front of the lens so that the size of the image is twice the size of the object? Also, calculate the power of the lens.
$(b)$ State the laws of refraction.

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 $, cm$)?

Draw a labelled ray diagram to locate the image of an object formed by a convex lens of focal length $20 \, cm$ when the object is placed $30 \, cm$ away from the lens.

An object $3 \, cm$ high is placed at a distance of $20 \, cm$ in front of a convex lens of focal length $12 \, cm$. Find the position,nature,and size of the image formed.