At the mouth of a cylindrical vessel, a convex lens of refractive index 1.5 and radius of curvature of curved surface 30 cm is filled. A point source S is at the bottom of vessel. The height of vessel is 40 cm and filled with liquid of refractive index 1.2. Find the position of image.

For refraction through spherical surface, μ1=1.2,μ2=1.5   r=+30cm,u=−40cm                ∵μ2v−μ1u=μ2−μ1t                         Or 1.5v−1.2−40=1.5−1.230  or  1.5v+12400=3300            Or 1.5v=1100−3100=-2100            Or  v=−1002×1.5=−75 cm            For refraction through spherical surface, μ1'=1.5,μ2'=1,u'=-75 cm,t'=-30                ∴μ2'v'−μ1'u'=μ2'−μ1't            Or 1v'+1.575=1-1.5-30            ∴v'=−300 cm