The distance between a real object and its real image formed by a converging lens is $56 \,cm$. The focal length $f$ of the lens is ............

When blue light is used instead of red light in a convex lens,its focal length will ......... .

Write the equation and definition of lateral magnification for a lens.

$A$ convex lens of glass $(\mu_g = 1.45)$ has a focal length $f_a$ in air. The lens is immersed in a liquid of refractive index $(\mu_l) = 1.3$. The ratio of the $f_l / f_a$ is

The diameter of the aperture of a plano-convex lens is $6 \, cm$ and its maximum thickness is $3 \, mm$. If the velocity of light in the material of the lens is $2 \times 10^8 \, m/s$,its focal length is ........ $cm$.

The following figure shows a beam of light converging at point $P$. When a concave lens of focal length $16 \,cm$ is introduced in the path of the beam at a place shown by the dotted line such that $OP$ becomes the axis of the lens,the beam converges at a distance $x$ from the lens. The value of $x$ will be equal to (in $\,cm$)