The optical power of a thin glass lens (refractive index $1.5$) in air is $-5 \ D$. What will be its optical power in a liquid with a refractive index of $1.6$ (in $D$)?

$A$ convex lens of focal length $25 \ cm$ and made of glass with refractive index $1.5$ is immersed in water. The absolute change in focal length of the glass is [Use refractive index of water = $\frac{4}{3}$] (in $cm$)

$A$ screen is placed $90 \, cm$ from an object. The image of the object is formed on the screen by a convex lens at two different locations separated by $20 \, cm$. If the sizes of the images formed at these positions are $6 \, cm$ and $3 \, cm$,then the height of the object is.....$cm$.

$A$ convex lens of focal length $f$ is placed somewhere in between an object and a screen. The distance between the object and the screen is $x$. If the numerical value of the magnification produced by the lens is $m$, then the focal length of the lens is

The focal length of a lens is greatest for which colour?

An object is placed at a distance of $5 \, cm$ from the first principal focus of a convex lens of focal length $10 \, cm$. If a real image is formed,find its distance from the lens in $cm$.