00:01
So i asked to find the mirror equation, starting with the equation that's given here in the chapter.
00:06
So you've got to do a couple things first, algebraically.
00:08
You've asked to solve it algebraically.
00:10
So i'm going to put the h and h prime's on the same side and the pq and r is on the same side of the equation.
00:17
So r minus q comes up to the numerator on the left -hand side over p -minus r equals negative h -prime stays divided by h.
00:25
Take that to the other side.
00:26
It goes to the denominator by division.
00:28
So this is what the equation looks like after that.
00:30
We recall from the chapter that negative h prime over h is the magnification, and that's equal to positive q over p.
00:40
So i can do a substitution into this equation.
00:42
You get r minus q over p minus r equals q over p.
00:50
And so it simplifies to that we're into the equation.
00:54
Then you know that focal length is equal to the radius of curvature over 2.
01:01
If i solve that for r, you get r equals twice the focal length.
01:05
So i can do a substitution back into this equation, and you get 2f minus q over p minus 2f equals q over p...