For an object placed at a distance $20 \ cm$ in front of a convex lens, the image is at a distance $20 \ cm$ behind the lens. The focal length of convex lens is:

Answer is B.

There is a geometrical relationship between the focal length of a lens $f$, the distance from the lens to the bright object $o$ and the distance from the lens to the projected image $i$. The relationship between the distances is given as $\dfrac { 1 }{ i } -\dfrac { 1 }{ o } =\dfrac { 1 }{ f }$.

It is given that object distance is -$20$ cm and the image distance is $20 cm$. So, the focal length is given as $\dfrac { 1 }{ 20 } +\dfrac { 1 }{ 20 } =\dfrac { 1 }{ 0.1 }$. The focal length $f=\dfrac { 1 }{ 0.1 } = 10 cm.$

The focal length of the lens is 10 cm.