A Plano convex lens has a thickness of $4 cm.$when placed on a horizontal table with 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 center of plane  face is found to be  $\frac{25}{8}\mathrm{cm}$. The focal length of the lens is (as measured from center of spherical surface) can be   

Let lens material is having $RI \mu$ & radius of curvature o/ spherical surface is $R$, then from given information 

$\mathrm{PI}=\frac{{\mathrm{P}}_0}{\mu }\Rightarrow 3=\frac{4}{\mu }\Rightarrow \mu =\frac{4}{3}$

Using  $\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\begin{array}{l}\Rightarrow \frac{1}{-25/8}-\frac{4/3}{-4}=\frac{1-4/3}{R}\\ \Rightarrow R=-25\mathrm{cm}\end{array}$

So radius of curvature is $25 cm$.

For focal length of thick lens we can't use the lens maker's formula so to find focal length here we have to proceed from basic approach. 

Case 1: 

When light is incident from plane face side, 

$\frac{1}{v}-\frac{4/3}{-\mathrm{\infty }}=\frac{-1/3}{-25}$

$\Rightarrow v=75\mathrm{cm}$

Case 2: 

When light is incident from curved side. 

For 1st refraction

$\frac{4/3}{v_1}-\frac{1}{\mathrm{\infty }}=\frac{1/3}{25}$

$\Rightarrow v_1=100\mathrm{cm}$

For $2^{\text{nd }}$ refraction 

$v=\frac{96}{4/3}=72\mathrm{cm}$

So require focal length $=72+4\mathrm{cm}=76\mathrm{cm}$.