$A$ thin glass (refractive index $1.5$) lens has an optical power of $-5\,D$ in air. Its optical power in a liquid medium with a refractive index of $1.6$ will be: (in $,D$)

An object is placed at a distance $m$ times the focal length of a divergent lens. The size of the image is shorter than that of the object by what factor?

$A$ diminished image of an object is to be obtained on a screen $1.0 \ m$ from it. This can be achieved by appropriately placing

The light gathering power of a camera lens depends on:

$f_V$ and $f_R$ are the focal lengths of a convex lens for violet and red light respectively,and $F_V$ and $F_R$ are the focal lengths of a concave lens for violet and red light respectively. Then:

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