What is the equation, and values of the constants and parameters in
that equation, for determining the force in Newtons on a mirror
occasioned by the reflection of a single photon of frequency f or
wavelength L?

We can imagine the reflection of a single photon  as ball bouncing
from a wall.
   Here are the    basic constants and equations
http://www.pa.msu.edu/~duxbury/courses/phy294H/lectures/lecture37/lecture37.html

  The force therefore  will be function of the  time F(t),
  being zero before the hit and after the hit, and having
 complex shape during the collision. Details of the shape
 depend on material of the mirror and geometry of the experiment.

 So there is not a single  number, giving answer in Newtons.
Summation of force over time will  add up double momentum of the
photon   p=h / wavelength which is in N * s .

 Here is a simulation of the process:
  Reflection of a photon wave packet on a mirror
up. Reflection of a photon wave packet on a mirror.
   http://quantum.quniverse.sk/buzek/simulations/Mirror.html  

Experiments involving single photons are difficult, but feasible
and recently of interest with applications in quantum cryptography.
  http://focus.aps.org/story/v8/st7  
      http://physicsweb.org/article/news/5/12/6/1

The  detailed process as function of time depends on the state of the
atom involved in the collision.
 physics.okstate.edu/summy/publications/jpb29.pdf

history of the effect    (light pressure)
http://www.europhysicsnews.com/full/07/article4/article4.html        


Search Term
single photon
photon momentum, reflection,

Momentum of a photon is h/lambda, where h=6.626*10-34 Joule-seconds.

To get force, you have multiply momentum by the number of
photons/second hitting the mirror.

And double it to account for reflection.

Or are you talking about relativisitic effects?

Now that I think about it more, I think there's too much probablistic
heisenbergish uncertanty eigen quantum crap involved with single
photons bouncing/reflecting off a mirror.  I would say "force is not
meaningful for single photons."  Momentum you can solve for, force you
can't.