$A$ particle executes linear $S.H.M.$ along the principal axis of a convex lens of focal length $8 \,cm$. The mean position of oscillation is at $14 \,cm$ from the lens with amplitude $1 \,cm$. The amplitude of the oscillating image of the particle is nearly: (in $\,cm$)

The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall $3\;m$ away by means of a large convex lens. What is the maximum possible focal length (in $m$) of the lens required for the purpose?

The dispersive powers of crown and flint glasses are $0.02$ and $0.04$ respectively. In an achromatic combination of lenses,the focal length of the flint glass lens is $40 \ cm$. The focal length of the crown glass lens will be $....... \ cm$.

$A$ magnifying lens has a focal length of $10 \, cm$. If the image is formed at a distance of $30 \, cm$ from the lens,what is the magnification?

$A$ thin lens made of glass (refractive index $= 1.5$) of focal length $f = 16 \; cm$ is immersed in a liquid of refractive index $1.42$. If its focal length in liquid is $f_{l}$,then the ratio $f_{l} / f$ is closest to the integer:

$A$ thin convex lens made from crown glass $\left( \mu = \frac{3}{2} \right)$ has focal length $f$. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$,it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal lengths is: