A ray of light is incident grazingly on a sphere of radius $R=10 \mathrm{cm}$ and $\mu =2.$ The $y$-coordinate, where the ray crosses $y$-axis is

 

A concave mirror of radius of curvature $R=40 \mathrm{cm}$ is placed inside water $\left(\mu =\frac{4}{3}\right)$ of depth $30 \mathrm{cm}.$ A parallel beam of light is incident on water surface as shown. The distance of final image is

A point object is placed in the arrangement shown. The distance of image formed by lens-$2$ from its optical centre is

An equiconvex lens $(\mu =1.5)$ of focal length $f=20 \mathrm{cm}$ is placed on a plane mirror. A liquid of $\mu =\frac{4}{3}$ is filled between the gap as shown. At what distance from the lens an object should be placed so that a virtual image of double the size of object is formed?