A planoconvex lens has thickness of 4 cm . When placed on a horizontal table, with the curved surface in contact with it, the apparent depth of the bottom most point of the lens is found to be 3 cm . If the lens is inverted such that the plane face is in contact with the table, the apparent depth of the centre of the plane face is found to be 25 8 cm . The focal length of the lens is (assume thickness of lens to be n

Step-by-step solution

In first case refraction of the rays, takes place from a plane surface, so we can use d app = d actual  μ 3 = 4 μ ⇒ μ = 4 3 where, d app  and d actual  = apparent and real depth, respectively. Now, in second case, as from Fig. (b), refraction takes place from a spherical surface, so μ 2 v - μ 1 u = μ 2 - μ 1 R m or 1 ( - 25 / 8 ) - 4 / 3 ( - 4 ) = 1 - 4 / 3 - R or 1 3 R = 1 3 - 8 25 = 1 75 R = 25   cm Now, using Lens' Makers formula, to calculate foca