Which of the following conditions must be satisfied to obtain a magnified image of an object using a concave mirror?

What is a 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.

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

What is meant by the radius of curvature of a spherical mirror? How is it related to the focal length of the mirror?

$(a)$ Two lenses have powers of $(i) +2 \text{ D}$ and $(ii) -4 \text{ D}$. What is the nature and focal length of each lens?
$(b)$ An object is kept at a distance of $100 \text{ cm}$ from a lens of power $-4 \text{ D}$. Calculate the image distance.