Derive the formula for normal shift or vertical shift in glass slab :
S = h(1-1/r)
[S=Normal shift]
[h=thickness of slab]
[r=refractive index of the medium]

Dear Student,
                                                                                                                                                      


$$\begin{gathered} so from figure \\ in triangleQPO \\ OP=QP\tan \left(i\right)=d\tan \left(i\right)----1 \\ OP=QA \\ in triangleQAB \\ AB=QA\tan (90-r)=d\tan \left(i\right)cot\left(r\right)=d\frac{\sin \left(i\right)}{\sin \left(r\right)} (as i and r very small) \\ now \\ OB=OA-AB=d-d\frac{\sin \left(i\right)}{\sin \left(r\right)}=d\left(1-\frac{1}{\mu }\right) \\ S=d\left(1-\frac{1}{\mu }\right) \end{gathered}$$
Regard