If the central portion of a convex lens is wrapped in black paper as shown in the figure,

Monochromatic light rays parallel to $x$-axis strike a convex lens $AB$. If the lens oscillates such that $AB$ tilts up to a small angle $\theta$ (in radian) on either side of $y$-axis,then the amplitude of oscillation of the image will be ($f =$ focal length of the lens):

Two point light sources are $24 \, cm$ apart. Where should a convex lens of focal length $9 \, cm$ be placed between them from one source so that the images of both the sources are formed at the same place (in $, cm$)?

$A$ concave lens (refractive index $n_l = 1.5$) has both surfaces of the same radius of curvature $R$. If it is immersed in a liquid of refractive index $n_m = 1.75$,it will act as a:

$A$ plano-convex lens is made of refractive index $1.6$. The radius of curvature of the curved surface is $60 \ cm$. The focal length of the lens is $..... \ cm$.

$(i)$ If $f=0.5 \,m$ for a glass lens,what is the power of the lens?
$(ii)$ The radii of curvature of the faces of a double convex lens are $10 \,cm$ and $15 \,cm$. Its focal length is $12 \,cm$. What is the refractive index of glass?
$(iii)$ $A$ convex lens has $20 \,cm$ focal length in air. What is its focal length in water? (Refractive index of water $= 1.33$,refractive index of glass $= 1.5$)