Questions about induced surface charge

[issacnewton]

Hi

I am reading Griffiths EM book and I have some questions about the induced surface charge
from chapter 2 and 3.

In chapter 2 , he says that

$$\frac{\partial V_{above} }{\partial n}- \frac{\partial V_{below} }{\partial n} = - \frac{\sigma}{\epsilon_o}...1)$$

which is alright. Now few sections later, he says that , just outside conductor, we have

$$\sigma =-\epsilon_o \frac{\partial V_{above} }{\partial n} ...2)$$

which is ok again. here the derivative of V inside the conductor is zero. Now
while discussing, method of image problem for a charge near a grounded conducting plane,
he again uses the same formula for the charge density. There we are considering a
plane , supposedly infinitesimally thin. Even though the plane is conducting,
we can't use the same arguments to arrive at eq. 2 from eq. 1. Can we ? What about
the other surface of this conducting plane ? Can we not talk of this part as below ?
and then the upper half (region where the actual charge is ) is above

 

[jbsteele]

?Can we do this ? if not, then how can we arrive at eq. 2 for the case of method of image problem ?Thanks