A transparent solid sphere of radius 2 cm and density p floats in a transparent liquid of density 2 rho kept in a beaker. The bottom of the beaker is spherical in shape with its radius of curvature 8 cm and is silvered to make it a concave mirror as shown in Fig. When an object is placed a 10 cm directly above the centre of the sphere its final image coincide with it. If 'h' is the height of liquid surface from the apex of the bottom as shown in figure. Consider paraxial rays only for image formation. The refractive index of the sphere is 3/2 and that of the liquid is 4/3 .Answer the following questions. The image formed by the top spherical portion of sphere is (as measured from top of spherical ball)

A convex lens is placed between an object and a screen which are a fixed distance apart. For one position of the lens the magnification of the image obtained on the screen is m_1 . When the lens is I moved by a distance d, the magnification of the image obtained on the same screen is m_2 . The focal length of the lens is (m_1 gt m_2)

A point object is placed infront of a plane mirror as shown in figure. X_(OM) rArr x - co-ordinate of object relative to mirror X_(IM) rArr x - x-co-ordinate of image relative to mirror X_(IM) = -X_(OM) differentiating V_(IM) = 0-V_(OM) V_I - V_M = - (V_0 - V_M) Velocity if image relative to mirror = velocity of object relative to mirror. basing on this information answer the questions A point object is moving with a speed v before an arrangement of two mirrors as shown in figure. The magnitude of velocity of image in mirror M_1 with respected to image in mirror M_2 is