Electric flux passing through a plane

[ViolentCorpse]

Homework Statement

Given a 60-μC point charge located at origin, find the total electric flux passing through the plane z = 26 cm.

Homework Equations

The Attempt at a Solution

Since electric flux lines from a point charge emanate in every possible direction, only a quarter of these should be passing through the plane which is "above" the point charge. So the flux should be 15-μC. But the answer given in my textbook is 30-μC. Half the total electric flux. I can't figure out why it's only half, because there are going to be a lot of flux lines parallel to the plane. When I asked my teacher about this he told me that it's half because parallel lines meet at infinity - which is something I've never heard of before - further aggravating my confusion...

I'll very much appreciate any help. Thank you for reading.

 

[haruspex]

there are going to be a lot of flux lines parallel to the plane.

There will be effectively none perfectly parallel to the plane. Even the slightest deviation from parallel will mean that the line either passes through the plane or gets ever further from it.

 

[ViolentCorpse]

I see. Thanks for your help, haruspex! :)