Where is the image formed when an object is placed at a distance of $2f$ in front of a convex mirror?

Through which of the following points will a ray passing through the centre of curvature and reflected by a concave mirror pass?

With respect to air,the refractive indices of ice and rock salt are $1.31$ and $1.54$ respectively. Calculate the refractive index of rock salt with respect to ice.

Discuss the position and nature of the image formed by a concave mirror when the object is moved from infinity towards the pole of the mirror.

$A$ student focussed the image of a candle flame on a white screen using a convex lens. He noted down the position of the candle,screen,and the lens as under:
Position of candle $= 12.0\, cm$
Position of convex lens $= 50.0\, cm$
Position of the screen $= 88.0\, cm$
$(i)$ Where will the image be formed if he shifts the candle towards the lens at a position of $31.0\, cm$?
$(ii)$ What will be the nature of the image formed if he further shifts the candle towards the lens?
$(iii)$ Draw a ray diagram to show the formation of the image in case $(ii)$ as said above.

What is a lens?