The focal length of a convex lens of refractive index $1.5$ is $2 \ cm$. What will be the focal length of the lens when it is immersed in a liquid of refractive index $1.25$?

$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is
$(a)$ a convex lens of focal length $20 \, cm$,and
$(b)$ a concave lens of focal length $16 \, cm$?

In the displacement method,there are two positions of a lens for which we get a clear image on a screen. If the first position of the lens is at $40 \, cm$ from the object and the second position is at $80 \, cm$ from the object,the focal length of the lens is ......... $cm$.

$A$ convex lens is used to form a real image of an object on a screen. It is observed that even when the positions of the object and the screen are fixed,there are two positions of the lens that form real images. If the heights of the images are $4 \ cm$ and $9 \ cm$ respectively,the height of the object is.....$cm$.

The focal length of a convex lens is $f$. An object is placed at a distance $x$ from its first focal point. The ratio of the size of the real image to that of the object is

$A$ 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