Coverage Area Of Light Reflected Using A Convex Mirror

[webmonk]

I have a real-world situation I need help with before I run out and spend money.

I have a wall that is in the shadows. I want to use a convex mirror to reflect sunlight onto the wall, covering as much of the surface area as possible. I will need a convex mirror with the right diameter and curvature to reflect sufficient light while covering the maximum amount of area. Here is the setup.

Let's say the wall is 25' wide by 10' high, and the mirrors will sit on posts 50' away.
If a 3' diameter flat mirror was reflecting sunlight, it would cover 7 sq ft of space and it would take roughly 35 of them to cover the entire wall. This is unacceptable. Let's say I wanted two mirrors to cover the wall. At 50' away, what would the center of curvature of a 3' diameter mirror need to be to cover 1/2 the space (10' x 12.5')?

How would the curvature change if the wall were say 80' away instead?

Hopefully that is enough information to go on. If not, post what additional information you need.

 

[haruspex]

You want each reflection to cover 10' x 10', roughly. At 50', that subtends an angle of about 11-12 degrees. So that's the amount of turn you need in the mirror as you cross from one side of it to the other. If the mirror has diameter 3' then its radius of curvature needs to be (3/2)cosec(12 deg/2) = 14.5 feet.