An equiconvex lens of focal length $f$ is cut into four equal parts and two parts are placed as shown in the figure. The focal length of the system shown in the figure is:

$A$ planoconvex lens becomes an optical system of $28 \, cm$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig $-A$. If the same lens is instead silvered on the curved surface and illuminated from the other side as in Fig. $-B$, it acts like an optical system of focal length $10 \, cm$. The refractive index of the material of the lens is

$A$ plano-convex lens made of material of refractive index $\mu$ with radius of curvature $R$ is silvered on the curved side. How far away from the lens-mirror must you place a point object,so that the image coincides with the object?

Consider a glass slab which is silvered at one side and the other side is transparent. The refractive index of the glass slab is $1.5$. If a ray of light is incident at an angle of $45^{\circ}$ on the transparent side,then the deviation of the ray of light from its initial path,when it comes out of the slab,is (in $^{\circ}$)

The radius of curvature of a lens is $20\,cm$ and its refractive index is $1.5$. If the refractive index of the surrounding liquid is $1.6$,then the focal length of the system is .......... $cm$.

$A$ thin equiconvex lens has a focal length of $10\; cm$ and a refractive index of $1.5$. One of its faces is now silvered,and for an object placed at a distance $u$ in front of the lens,the image coincides with the object. The value of $u$ is: (in $; cm$)