Wedge calculator (Koji Arai, 11-16-2009)

2deg wedge, t=25mm

User Inputs

(* The reflactive indices are for Corning 7980 *)
n1064=1.4496;
n532=1.4608;

(* Choose IR or Green *)
n=n1064;

(* Define wedge angle *)
wdeg=2; (* degree *)

(* Average thickness of the mirror *)
t = 0.025; (* meter *)

(* Origin of the beam *)
X0={0,-0.01};

(* Incident angle of the initial beam *)
θdeg = 0.; (* incident angle *)

(* for displayig purpose *)
l=0.01;

Calculation

Preparation

(* Convert angles to rad *)
{w,θ}={wdeg,θdeg}/180*Pi;

(* Ray vector for X0-X1 *)
dX01={Sin[θ],Cos[θ]};

Solve X1

(* equation for X1 *)
X1=X0-a1  dX01;
(* find Y=0 solution *)
sola1=Solve[X1[[2]]==0];
(* substitute X1 *)
X1=X1/.sola1[[1]];

Solve X2

(* angle of the X1-X2 beam ~ snell's law *)
α=ArcSin[Sin[θ]/n];
(* Ray vector for X1-X2 *)
dX12={Sin[α],Cos[α]};
(* equation for X2 *)
X2=X1 -a2 dX12;
(* find solution with the wedged surface *)
sola2=Solve[X2=={0,t}-b2 {1,w},a2,b2];
(* substitute X2 *)
X2=X2 /. sola2[[1]];

Solve X3

(* angle of the X2-X3 beam *)
β=ArcSin[Sin[α+w]*n]-w;
(* Ray vector for X2-X3 *)
dX23={Sin[β],Cos[β]};
(* Put X3 at distance l *)
X3=X2+l dX23;

Solve X4

(* angle of the X2-X4 beam *)
γ=β-(β+w)*2;
(* Ray vector for X2-X4 *)
dX24={Sin[γ],Cos[γ]};
(* Put X3 at distance l *)
X4=X2+l dX24;

Solve X5

(* angle of the X2-X5 beam *)
δ=-α+(α+w)*2;
(* Ray vector for X2-X4 *)
dX25={Sin[δ],-Cos[δ]};
(* equation for X5 *)
X5=X2+a3 dX25;
(* find solution for Y=0 *)
sola3=Solve[X5[[2]]==0];
(* substitute X5 *)
X5=X5/.sola3[[1]];

Solve X6

(* Ray vector for X5-X6 ~ Mirror X2-X5 beam *)
dX56={Sin[δ],Cos[δ]};
(* equation for X6 *)
X6=X5+dX56*a4;
(* find solution with the wedged surface *)
sola4=Solve[X6=={0,t}-b2 {1,w},a4,b2];
(* substitute X6 *)
X6=X6 /. sola4[[1]];

Solve X7

(* angle of the X6-X7 beam *)
ϵ=ArcSin[Sin[δ+w]*n]-w;
(* Ray vector for X6-X7 *)
dX67={Sin[ϵ],Cos[ϵ]};
(* Put X7 at distance l *)
X7=X6+l dX67;

Result

Graphics[
{
{Point[{X0,X1,X2,X3,X4,X5,X6,X7}]},
{RGBColor[1,0,0],Line[{X0,X1,X2,X3}]},
{RGBColor[1,0,0],Line[{X2,X4}]},
{RGBColor[1,0,0],Line[{X2,X5,X6,X7}]},
{RGBColor[0,0,0],Line[{{-0.01,0},{0.01,0}}]},
{RGBColor[0,0,0],Line[{{-0.01,t-0.01w},{0.01,t+0.01w}}]}
},
Frame->True
]

(* Coordinates for X1~X7 *)
TableForm[{X0,X1,X2,X3,X4,X5,X6,X7}]

(*Angles of the rays in degree *)
TableForm[{α,β,γ,δ,ϵ}/Pi*180]

2deg wedge, t=10mm

User Inputs

(* The reflactive indices are for Corning 7980 *)
n1064=1.4496;
n532=1.4608;

(* Choose IR or Green *)
n=n1064;

(* Define wedge angle *)
wdeg=2; (* degree *)

(* Average thickness of the mirror *)
t = 0.010; (* meter *)

(* Origin of the beam *)
X0={0,-0.01};

(* Incident angle of the initial beam *)
θdeg = 0.; (* incident angle *)

(* for displayig purpose *)
l=0.01;

Calculation

Preparation

(* Convert angles to rad *)
{w,θ}={wdeg,θdeg}/180*Pi;

(* Ray vector for X0-X1 *)
dX01={Sin[θ],Cos[θ]};

Solve X1

(* equation for X1 *)
X1=X0-a1  dX01;
(* find Y=0 solution *)
sola1=Solve[X1[[2]]==0];
(* substitute X1 *)
X1=X1/.sola1[[1]];

Solve X2

(* angle of the X1-X2 beam ~ snell's law *)
α=ArcSin[Sin[θ]/n];
(* Ray vector for X1-X2 *)
dX12={Sin[α],Cos[α]};
(* equation for X2 *)
X2=X1 -a2 dX12;
(* find solution with the wedged surface *)
sola2=Solve[X2=={0,t}-b2 {1,w},a2,b2];
(* substitute X2 *)
X2=X2 /. sola2[[1]];

Solve X3

(* angle of the X2-X3 beam *)
β=ArcSin[Sin[α+w]*n]-w;
(* Ray vector for X2-X3 *)
dX23={Sin[β],Cos[β]};
(* Put X3 at distance l *)
X3=X2+l dX23;

Solve X4

(* angle of the X2-X4 beam *)
γ=β-(β+w)*2;
(* Ray vector for X2-X4 *)
dX24={Sin[γ],Cos[γ]};
(* Put X3 at distance l *)
X4=X2+l dX24;

Solve X5

(* angle of the X2-X5 beam *)
δ=-α+(α+w)*2;
(* Ray vector for X2-X4 *)
dX25={Sin[δ],-Cos[δ]};
(* equation for X5 *)
X5=X2+a3 dX25;
(* find solution for Y=0 *)
sola3=Solve[X5[[2]]==0];
(* substitute X5 *)
X5=X5/.sola3[[1]];

Solve X6

(* Ray vector for X5-X6 ~ Mirror X2-X5 beam *)
dX56={Sin[δ],Cos[δ]};
(* equation for X6 *)
X6=X5+dX56*a4;
(* find solution with the wedged surface *)
sola4=Solve[X6=={0,t}-b2 {1,w},a4,b2];
(* substitute X6 *)
X6=X6 /. sola4[[1]];

Solve X7

(* angle of the X6-X7 beam *)
ϵ=ArcSin[Sin[δ+w]*n]-w;
(* Ray vector for X6-X7 *)
dX67={Sin[ϵ],Cos[ϵ]};
(* Put X7 at distance l *)
X7=X6+l dX67;

Result

Graphics[
{
{Point[{X0,X1,X2,X3,X4,X5,X6,X7}]},
{RGBColor[1,0,0],Line[{X0,X1,X2,X3}]},
{RGBColor[1,0,0],Line[{X2,X4}]},
{RGBColor[1,0,0],Line[{X2,X5,X6,X7}]},
{RGBColor[0,0,0],Line[{{-0.01,0},{0.01,0}}]},
{RGBColor[0,0,0],Line[{{-0.01,t-0.01w},{0.01,t+0.01w}}]}
},
Frame->True
]

(* Coordinates for X1~X7 *)
TableForm[{X0,X1,X2,X3,X4,X5,X6,X7}]

(*Angles of the rays in degree *)
TableForm[{α,β,γ,δ,ϵ}/Pi*180]

2.5deg wedge, t=25mm, 45 deg (Part 1)

User Inputs

(* The reflactive indices are for Corning 7980 *)
n1064=1.4496;
n532=1.4608;

(* Choose IR or Green *)
n=n1064;

(* Define wedge angle *)
wdeg=2.5; (* degree *)

(* Average thickness of the mirror *)
t = 0.025; (* meter *)

(* Origin of the beam *)
X0={-0.01,-0.01};

(* Incident angle of the initial beam *)
θdeg = 45.; (* incident angle *)

(* for displayig purpose *)
l=0.01;

Calculation

Preparation

(* Convert angles to rad *)
{w,θ}={wdeg,θdeg}/180*Pi;

(* Ray vector for X0-X1 *)
dX01={Sin[θ],Cos[θ]};

Solve X1

(* equation for X1 *)
X1=X0-a1  dX01;
(* find Y=0 solution *)
sola1=Solve[X1[[2]]==0];
(* substitute X1 *)
X1=X1/.sola1[[1]];

Solve X2

(* angle of the X1-X2 beam ~ snell's law *)
α=ArcSin[Sin[θ]/n];
(* Ray vector for X1-X2 *)
dX12={Sin[α],Cos[α]};
(* equation for X2 *)
X2=X1 -a2 dX12;
(* find solution with the wedged surface *)
sola2=Solve[X2=={0,t}-b2 {1,w},a2,b2];
(* substitute X2 *)
X2=X2 /. sola2[[1]];

Solve X3

(* angle of the X2-X3 beam *)
β=ArcSin[Sin[α+w]*n]-w;
(* Ray vector for X2-X3 *)
dX23={Sin[β],Cos[β]};
(* Put X3 at distance l *)
X3=X2+l dX23;

Solve X4

(* angle of the X2-X4 beam *)
γ=β-(β+w)*2;
(* Ray vector for X2-X4 *)
dX24={Sin[γ],Cos[γ]};
(* Put X3 at distance l *)
X4=X2+l dX24;

Solve X5

α

w//N

(* angle of the X2-X5 beam *)
δ=-α+(α+w)*2;
(* Ray vector for X2-X4 *)
dX25={Sin[δ],-Cos[δ]};
(* equation for X5 *)
X5=X2+a3 dX25;
(* find solution for Y=0 *)
sola3=Solve[X5[[2]]==0];
(* substitute X5 *)
X5=X5/.sola3[[1]];

Solve X6

(* Ray vector for X5-X6 ~ Mirror X2-X5 beam *)
dX56={Sin[δ],Cos[δ]};
(* equation for X6 *)
X6=X5+dX56*a4;
(* find solution with the wedged surface *)
sola4=Solve[X6=={0,t}-b2 {1,w},a4,b2];
(* substitute X6 *)
X6=X6 /. sola4[[1]];

Solve X7

(* angle of the X6-X7 beam *)
ϵ=ArcSin[Sin[δ+w]*n]-w;
(* Ray vector for X6-X7 *)
dX67={Sin[ϵ],Cos[ϵ]};
(* Put X7 at distance l *)
X7=X6+l dX67;

Result

Graphics[
{
{Point[{X0,X1,X2,X3,X4,X5,X6,X7}]},
{RGBColor[1,0,0],Line[{X0,X1,X2,X3}]},
{RGBColor[1,0,0],Line[{X2,X4}]},
{RGBColor[1,0,0],Line[{X2,X5,X6,X7}]},
{RGBColor[0,0,0],Line[{{-0.01,0},{0.01,0}}]},
{RGBColor[0,0,0],Line[{{-0.01,t-0.01w},{0.01,t+0.01w}}]}
},
Frame->True
]

(* Coordinates for X1~X7 *)
TableForm[{X0,X1,X2,X3,X4,X5,X6,X7}]

(*Angles of the rays in degree *)
TableForm[{α,β,γ,δ,ϵ}/Pi*180]

2.5deg wedge, t=25mm, 45 deg (Part 2)

User Inputs

(* The reflactive indices are for Corning 7980 *)
n1064=1.4496;
n532=1.4608;

(* Choose IR or Green *)
n=n1064;

(* Define wedge angle *)
wdeg=2.5; (* degree *)

(* Average thickness of the mirror *)
t = 0.025; (* meter *)

(* Origin of the beam *)
X0={0.01,-0.01};

(* Incident angle of the initial beam *)
θdeg = -45.; (* incident angle *)

(* for displayig purpose *)
l=0.01;

Calculation

Preparation

(* Convert angles to rad *)
{w,θ}={wdeg,θdeg}/180*Pi;

(* Ray vector for X0-X1 *)
dX01={Sin[θ],Cos[θ]};

Solve X1

(* equation for X1 *)
X1=X0-a1  dX01;
(* find Y=0 solution *)
sola1=Solve[X1[[2]]==0];
(* substitute X1 *)
X1=X1/.sola1[[1]];

Solve X2

(* angle of the X1-X2 beam ~ snell's law *)
α=ArcSin[Sin[θ]/n];
(* Ray vector for X1-X2 *)
dX12={Sin[α],Cos[α]};
(* equation for X2 *)
X2=X1 -a2 dX12;
(* find solution with the wedged surface *)
sola2=Solve[X2=={0,t}-b2 {1,w},a2,b2];
(* substitute X2 *)
X2=X2 /. sola2[[1]];

Solve X3

(* angle of the X2-X3 beam *)
β=ArcSin[Sin[α+w]*n]-w;
(* Ray vector for X2-X3 *)
dX23={Sin[β],Cos[β]};
(* Put X3 at distance l *)
X3=X2+l dX23;

Solve X4

(* angle of the X2-X4 beam *)
γ=β-(β+w)*2;
(* Ray vector for X2-X4 *)
dX24={Sin[γ],Cos[γ]};
(* Put X3 at distance l *)
X4=X2+l dX24;

Solve X5

α

w//N

(* angle of the X2-X5 beam *)
δ=-α+(α+w)*2;
(* Ray vector for X2-X4 *)
dX25={Sin[δ],-Cos[δ]};
(* equation for X5 *)
X5=X2+a3 dX25;
(* find solution for Y=0 *)
sola3=Solve[X5[[2]]==0];
(* substitute X5 *)
X5=X5/.sola3[[1]];

Solve X6

(* Ray vector for X5-X6 ~ Mirror X2-X5 beam *)
dX56={Sin[δ],Cos[δ]};
(* equation for X6 *)
X6=X5+dX56*a4;
(* find solution with the wedged surface *)
sola4=Solve[X6=={0,t}-b2 {1,w},a4,b2];
(* substitute X6 *)
X6=X6 /. sola4[[1]];

Solve X7

(* angle of the X6-X7 beam *)
ϵ=ArcSin[Sin[δ+w]*n]-w;
(* Ray vector for X6-X7 *)
dX67={Sin[ϵ],Cos[ϵ]};
(* Put X7 at distance l *)
X7=X6+l dX67;

Result

Graphics[
{
{Point[{X0,X1,X2,X3,X4,X5,X6,X7}]},
{RGBColor[1,0,0],Line[{X0,X1,X2,X3}]},
{RGBColor[1,0,0],Line[{X2,X4}]},
{RGBColor[1,0,0],Line[{X2,X5,X6,X7}]},
{RGBColor[0,0,0],Line[{{-0.01,0},{0.01,0}}]},
{RGBColor[0,0,0],Line[{{-0.01,t-0.01w},{0.01,t+0.01w}}]}
},
Frame->True
]

(* Coordinates for X1~X7 *)
TableForm[{X0,X1,X2,X3,X4,X5,X6,X7}]

(*Angles of the rays in degree *)
TableForm[{α,β,γ,δ,ϵ}/Pi*180]