Which of the lenses with focal lengths $10 \, cm$,$20 \, cm$,$25 \, cm$,and $50 \, cm$ has the maximum power (in $, cm$)?

$A$ 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.

At what distance should an object be placed to obtain its real,inverted and of same size image as the object by a convex lens?

$(a)$ $A$ 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 $, cm$)?

$A$ point object is placed at a distance of $12 \, cm$ from a convex lens on its principal axis. Its image is formed on the other side of the lens at a distance of $18 \, cm$ from the lens. Find the focal length of the lens. Is the image magnified? Justify your answer.