Maple/Depth of field for optical lens

> restart; > NULL; > > e1 := (vn-v)/vn = c/d:

> e2 := (v-vf)/vf = c/d:

> e3 := N = f/d:

> e4 := 1/Dn+1/vn = 1/f:

> e5 := 1/Df+1/vf = 1/f:

> e6 := 1/s+1/v = 1/f:

> sys := {e1, e2, e3, e4, e5, e6}; #Set of 6 equations

>var := {Df, Dn, d, v, vf, vn}; #6 variables

>sol := solve(sys,var); #solve the equation set

Find hyperfocal distance

> tm3 := 1/op(op(sol)[1])[2] = 0;

> tm4 := H = solve(tm3, s); f (f + c N)                       H = --- c N   > > eqf := {tm4, op(sol)[1], op(sol)[2]};

varf := {Df, Dn, c}; /              2                          2               |            s f                        s f               < Df = --, Dn = - ---, |     2                           2                       \     f  + c N f - c N s         -f  + c N f - c N s

\          f (f + c N)| H = --- > c N   | /                          {Df, Dn, c}

eqf:= {$$Df=\frac{s*f^2}{f^2+cNf-cNs}$$,$$Dn=\frac{s*f^2}{-f^2+cNf-cNs)}$$,$$H=f+\frac{f^2}{Nc}$$};

> solve(eqf, varf); /                                         2    \        |     s (H - f)        s (H - f)          f     | < Df = -, Dn = ---, c = - > |      H - s         H - 2 f + s      N (H - f)| \                                              / >