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


> solve(eqf, varf);

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


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