Give one use of a concave lens.

$A$ thin lens has a focal length of $-12\, cm$. Is it a convex lens or a concave lens?

$A$ 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.

$A$ 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.

$A$ doctor has prescribed a corrective lens of power $+1.5\, D.$ Find the focal length of the lens. Is the prescribed lens diverging or converging?

$A$ convex lens of focal length $20 \, cm$ can produce a magnified virtual as well as real image. Is this a correct statement? If yes,where shall the object be placed in each case for obtaining these images?